System, method and apparatus for non-mechanical optical and photonic beam steering

ABSTRACT

An example system includes a bulk steering crystal apparatus having a first lens face and a second concave face. The example bulk steering crystal apparatus further includes a number of steering portions interposed between the first lens face and the second concave face, where each of the steering portions includes a bulk substrate portion including an electro-optical material and a corresponding high-side electrode electrically coupled to the corresponding one of the number of steering portions.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/US19/57616, filed Oct. 23, 2019, entitled “SYSTEM, METHOD ANDAPPARATUS FOR NON-MECHANICAL OPTICAL AND PHOTONIC BEAM STEERING(EXCT-0004-WO).

PCT/US19/57616, filed Oct. 23, 2019 (EXCT-0004-WO) claims priority toU.S. Provisional Patent Application No. 62/868,286, filed on Jun. 28,2019, entitled “SYSTEM, METHOD AND APPARATUS FOR NON-MECHANICAL OPTICALAND PHOTONIC BEAM STEERING” (EXCT-0005-P01). PCT/US19/57616, filed Oct.23, 2019 (EXCT-0004-WO) also claims priority to U.S. Provisional PatentApplication No. 62/749,487, filed on Oct. 23, 2018, entitled “SYSTEM,METHOD AND APPARATUS FOR NON-MECHANICAL OPTICAL AND PHOTONIC BEAMSTEERING” (EXCT-0002-P01). PCT/US19/57616, filed Oct. 23, 2019(EXCT-0004-WO) further claims priority to, and is a continuation-in-partof, PCT application PCT/US19/23915, filed on Mar. 25, 2019, and entitled“SYSTEM, METHOD AND APPARATUS FOR NON-MECHANICAL OPTICAL AND PHOTONICBEAM STEERING” (EXCT-0003-WO).

Each of the foregoing applications is incorporated herein by referencein the entirety for all purposes.

BACKGROUND

Previously known beam steering systems and methods suffer from a numberof drawbacks. Mechanically steered systems have a number of movingparts, manufacturing cost and complexity, and have limitations in theresponse time of the system to effect a beam steering change.Additionally, mechanical systems suffer from reliability issues relatedto mechanical failures. Previously known beam steering systems withoutmechanical steering additionally suffer from a number of drawbacks,including limited steering capability, limited steering efficiency, andhigh voltage differences occurring within the devices.

Operations of a typical previously known beam steering system aredescribed following. a previously known beam steering system includes afilm of optically active material positioned between a ground electrodeand discrete electrodes with voltages applied. The voltages start fromzero, increase to a designed voltage over a number of electrodes, andthen reset to zero. The discrete electrodes are separated by a spacingdistance, which may be the same throughout the aperture (i.e., acrossthe entire film). The designed voltage will be V_lambda, or the voltagesufficient to provide one optical path difference (OPD) of onewavelength, and will depend upon the properties of the film and theincident wavelength being steered. The voltages applied between adjacentdiscrete electrodes will be progressive, depending upon how manydiscrete electrodes are utilized to progress from zero voltage to theV_lambda, except between reset electrodes. At the reset electrodes, thevoltage difference would be approximately V_lambda—with a V_lambdavoltage on a last discrete electrode of one progression, andapproximately zero voltage on a first discrete electrode of the nextprogression, with a separation of 2πn before and after reset. Theapplied electric field is not confined between each discrete electrodeand the ground electrode, and further the applied electric field is notparallel outside of the spacing between each discrete electrode and theground electrode. Accordingly, previously known beam steering systemsexperience an edge effect and a fringing field causing large steeringefficiency losses at the reset position, where the voltage cannot resetsharply to 0V. The distance required to reset to zero is the flybackdistance, which can be large in previously known beam steering systems,and can extend across several electrode widths.

Accordingly, improvements in beam steering systems, including systemswith limited or no mechanical moving parts, are desirable.

SUMMARY OF THE DISCLOSURE

An example system includes a bulk steering crystal apparatus having afirst lens face and a second concave face, and a number of steeringportions interposed between the first lens face and the second concaveface, where each of the number of steering portions includes a bulksubstrate portion including an electro-optical material, and acorresponding high-side electrode electrically coupled to thecorresponding one of the number of steering portions.

Certain further aspects of the example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes where each of the corresponding high-sideelectrodes are positioned on a side of the bulk steering crystal, and/ora low-side electrode positioned on an opposing side of the bulk steeringcrystal to at least one of the corresponding high-side electrodes. Anexample system includes where each of the corresponding high-sideelectrodes are positioned on a same side of the bulk steering crystal; alow-side electrode positioned on an opposing side of the bulk steeringcrystal; where the low-side electrode is positioned as the low-sideelectrode for a number of the steering portions; and/or where thelow-side electrode is positioned as the low-side electrode for all ofthe steering portions.

An example system further includes a bulk steering circuit structured tointerpret a steering command value, and to provide voltage commands toeach of the corresponding high-side electrodes in response to thesteering command value; a low-side electrode positioned on an opposingside of the bulk steering crystal to at least one of the correspondinghigh-side electrodes, and where the bulk steering circuit is furtherstructured to provide a low-side voltage command to the low-sideelectrode in response to the steering command value; where the low-sidevoltage command includes a negative voltage value, and where acorresponding high-side voltage command includes a positive voltagevalue; and/or where the low-side voltage command includes a samemagnitude as the corresponding high-side voltage command.

An example system further includes a first portion of the number ofsteering portions configured to steer an incident electromagnetic (EM)beam in a first axis, and a second portion of the number of steeringportions configured to steer the incident EM beam in a second axis;where the bulk substrate portions corresponding to the first portion ofthe number of steering portions are oriented in a first direction, andwherein the bulk substrate portions corresponding to the second portionof the number of steering portions are oriented in a second direction;where the bulk substrate portions corresponding to the first portion ofthe number of steering portions are traversed by the incident EM beambefore the second portion of the number of steering portions; ananti-reflective coating optically interposed between an interface of atleast one of the bulk substrate portions corresponding to the firstportion of the number of steering portions and at least one of the bulksubstrate portions corresponding to the second portion of the number ofsteering portions; where the bulk substrate portions corresponding tothe first portion of the number of steering portions are traversed bythe incident EM beam before the second portion of the number of steeringportions; at least one of an anti-reflective coating or a half-waveplate optically interposed between an interface of at least one of thebulk substrate portions corresponding to the first portion of the numberof steering portions and at least one of the bulk substrate portionscorresponding to the second portion of the number of steering portions;and/or where the concave face includes at least one shape such as aspherical cap, an ellipsoid cap, a hyperboloid cap, and/or an ellipticparaboloid cap. An example system includes the concave face having atleast one shape such as a circular cross-section; a paraboliccross-section; a hyperbolic cross-section; and/or rotations of any oneof the foregoing.

An example system further includes a varifocal lens (VFL) positioned atthe first lens face, and a VFL circuit structured to provide a voltagegradient command in response to the steering command value. In certainfurther embodiments, the example system includes where the VFL circuitis further structured to determine a beam divergence value in responseto the steering command value, and to provide the voltage gradientcommand further in response to the steering command value; where the VFLcircuit is further structured to determine a VFL temperature valuecorresponding to the VFL, and to provide the voltage gradient commandfurther in response to the VFL temperature value; where the bulksteering circuit is further structured to determine a bulk crystaltemperature value corresponding to at least one of the bulk steeringportions, and to provide the voltage commands to each of thecorresponding high-side electrodes further in response to the bulkcrystal temperature value; and/or where a low-side electrode ispositioned on an opposing side of the bulk steering crystalcorresponding to the at least one of the bulk steering portions, andwhere the bulk steering circuit is further structured to provide alow-side voltage command to the low-side electrode in response to thesteering command value and the bulk crystal temperature value.

An example system includes where the bulk steering portions include anincreasing width in at least a steered axis, and/or where the increasingwidth is monotonically increasing between the first lens face and thesecond concave face. An example system includes the VFL including a VFLsubstrate including an electro-optical material, a transparent low-sideelectrode positioned on a first side of the VFL substrate, and ahigh-side electrode positioned in electrical proximity to a second sideof the VFL substrate. In certain further embodiments, the example VFLfurther includes where the high-side electrode includes a closed loopelectrode positioned on the second side of the VFL substrate; where theclosed loop electrode is a symmetrically closed loop; where the closedloop electrode is at least one of a circular electrode or an ellipticalelectrode; where the high-side electrode includes a first high-sideelectrode positioned along a first edge of a viewing area of the VFLsubstrate, and a second high-side electrode positioned along a secondedge of the viewing area of the VFL substrate; where the first high-sideelectrode and the second high-side electrode are positioned outside anoptical path of the viewing area of the VFL substrate; where the firsthigh-side electrode and the second high-side electrode are positionedwithin an optical path of the viewing area of the VFL substrate; wherethe first high-side electrode and the second high-side electrode aretransparent; where the VFL circuit is further structured to provide thevoltage gradient command by commanding a first voltage value to thefirst high-side electrode, and by commanding a second voltage value tothe second high-side electrode; where the first voltage value and thesecond voltage value have an equal magnitude, and an opposite sign;where the VFL circuit is further structured to provide the voltagegradient by commanding a third voltage value to the transparent low-sideelectrode; and/or where the VFL substrate includes a solid material. Anexample system includes one or more bulk substrate portions including asolid material.

An example apparatus includes a thin beam steering device, including aconvex lens portion optically coupled to the thin beam steering deviceon a first side of the thin beam steering device, and a concave lensportion optically coupled to the thin beam steering device on a secondside of the thin beam steering device. Certain further aspects of theexample apparatus are described following, any one or more of which maybe present in certain embodiments.

An example apparatus includes where the thin beam steering deviceincludes at least one configuration such as: a castle scanner, a castlescanner pro, a chess scanner, and a chess scanner pro. An exampleapparatus includes where the thin beam steering device utilizes ahalf-wave voltage profile; where the apparatus is capable to steer anincident electromagnetic beam to a range of at least +/−20 degrees inone axis; where the apparatus is capable to steer an incidentelectromagnetic beam to a range of at least +/−30 degrees in one axis;where the convex lens portion and the concave lens portion each areformed from separate substrates; where the separate substrates areformed utilizing manufacturing techniques having similar tolerancevalues; and/or where the convex lens portion and the concave lensportion include a shared substrate.

Another example system includes a beam steering crystal including anelectro-optical material, a first lens positioned in opticalcommunication with the beam steering crystal, a second lens positionedin optical communication with the first lens, where the second lens isoptically interposed between the first lens and the beam steeringcrystal, and a beam steering circuit structured to adjust a voltage dropacross the beam steering crystal, and thereby steer an electro-magnetic(EM) beam incident on the beam steering crystal. Certain further aspectsof the example system are described following, any one or more of whichmay be present in certain embodiments.

The example system includes where at least one of the first lens or thesecond lens include a varifocal lens (VFL), and/or where the VFLincludes an electro-optical material electrically coupled to a high-sideelectrode and a low-side electrode, and wherein the beam steeringcircuit is further structured to adjust a focal length of the at leastone of the first lens or the second lens.

Another example apparatus includes a bulk substrate including anelectro-optical material, a transparent low-side electrode positioned ona first side of the bulk substrate, a high-side electrode positioned inelectrical proximity to a second side of the bulk substrate, and avarifocal lens (VFL) circuit structured to adjust a voltage gradientacross the bulk substrate, thereby operating the bulk substrate as aVFL. Certain further aspects of the example apparatus are describedfollowing, any one or more of which may be present in certainembodiments.

An example apparatus further includes where the high-side electrodeincludes a closed loop electrode positioned on the second side of thebulk substrate; where the closed loop electrode includes a symmetricallyclosed loop; where the closed loop electrode includes a circularelectrode; where the high-side electrode includes a first high-sideelectrode positioned along a first edge of a viewing area of the bulksubstrate, and a second high-side electrode positioned along a secondedge of the viewing area of the bulk substrate; where the firsthigh-side electrode and the second high-side electrode are positionedoutside an optical path of the viewing area of the bulk substrate; wherethe first high-side electrode and the second high-side electrode arepositioned within an optical path of the viewing area of the bulksubstrate; where the first high-side electrode and the second high-sideelectrode are transparent; where the VFL circuit is further structuredto adjust the voltage gradient by commanding a first voltage value tothe first high-side electrode, and by commanding a second voltage valueto the second high-side electrode; where the first voltage value and thesecond voltage value have an equal magnitude, and an opposite sign;where the VFL circuit is further structured to adjust the voltagegradient by commanding a third voltage value to the transparent low-sideelectrode; and/or where the bulk substrate includes a solid material.

Another example system includes a pair of opposing varifocal lenses(VFLs) having a spacing distance therebetween, a VFL circuit structuredto steer an electromagnetic (EM) beam incident on a first one of thepair of opposing VFLs, and where the steering operation of the VFLcircuit includes the VFL circuit further structured to control a firstfocal length corresponding to the first one of the pair of opposing VFLsand a second focal length corresponding to a second one of the pair ofopposing VFLs. Certain further aspects of the example system aredescribed following, any one or more of which may be present in certainembodiments.

An example system further includes a pair of opposing gap extensionlenses, where the pair of opposing gap extension lenses are opticallyinterposed between the pair of opposing VFLs; a first gap between afirst one of the pair of opposing gap extension lenses and the first oneof the pair of opposing VFLs, a second gap between the first one of thepair of opposing gap extension lenses and a second one of the pair ofopposing gap extension lenses, and a third gap between the second one ofthe pair of opposing gap extension lenses and the second one of the pairof opposing VFLs, where the third gap is a largest member of the firstgap, the second gap, and the third gap; where at least one of the pairof opposing gap extension lenses includes a VFL; where the pair ofopposing gap extension lenses are configured such that the EM beamincident on the first one of the pair of opposing VFLs is directed tothe second one of the pair of opposing VFLs; where the pair of opposinggap extension lenses are further configured such that the EM beamincident on the first one of the pair of opposing VFLs is directed tothe second one of the pair of opposing VFLs through a selected range ofsteering angles; where the pair of opposing gap extension lenses arefurther configured such that the EM beam incident on the first one ofthe pair of opposing VFLs is directed to the second one of the pair ofopposing VFLs through a selected range of incident angles; where the VFLcircuit is further structured to adjust at least one gap extension focallength corresponding to at least one of the pair of opposing gapextension VFLs such that the EM beam incident on the first one of thepair of opposing VFLs is directed to the second one of the pair ofopposing VFLs; where the VFL circuit is further structured to adjust atleast one gap extension focal length corresponding to at least one ofthe pair of opposing gap extension VFLs such that the EM beam incidenton the first one of the pair of opposing VFLs is directed to the secondone of the pair of opposing VFLs through a selected range of steeringangles; and/or where the VFL circuit is further structured to adjust atleast one gap extension focal length corresponding to at least one ofthe pair of opposing gap extension VFLs such that the EM beam incidenton the first one of the pair of opposing VFLs is directed to the secondone of the pair of opposing VFLs through a selected range of incidentangles.

An example procedure for steering an incident electromagnetic (EM) beamincludes an operation to apply a selected convergence amount to anincident EM beam at a lens face of a bulk steering crystal, an operationto progressively steer the incident EM beam through a number of steeringportions of the bulk steering crystal, and an operation to emit theincident EM beam from a concave face of the bulk steering crystal.Certain further aspects of the example procedure are describedfollowing, any one or more of which may be present in certainembodiments.

An example procedure further includes compensating the selectedconvergence amount to a divergence value of the EM beam; operating avarifocal lens (VFL) to apply the selected convergence amount;compensating an applied voltage to the VFL in response to a temperatureof the VFL; where operating the VFL includes applying a voltage gradientto a VFL substrate; where applying the voltage gradient to the VFLsubstrate includes applying a quadratic index gradient across the VFLsubstrate; where applying the voltage gradient to the VFL substratefurther includes applying a positive voltage to one side of the VFLsubstrate, and a negative voltage to the other side of the VFLsubstrate; progressively steering the incident EM beam through thenumber of steering portions by applying a selected voltage differentialacross each of the number of steering portions; compensating theselected voltage differentials in response to at least one of atemperature value for the bulk crystal or a temperature value for one ofthe number of steering portions; where applying the selected convergenceamount includes operating a VFL substrate in a paraelectric region;where the progressively steering includes operating at least one of thenumber of steering portions in a paraelectric region; and/or where theprogressively steering comprises operating at least one of the number ofsteering portions in a ferroelectric region.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows a graph depicting modulo 2π phase shifting to create beamsteering.

FIG. 2 shows a graph depicting the effect of fringing fields on phaseprofile associated for a previously known electro optical thin filmscanner.

FIG. 3 is a plan view of a previously known bulk beam steering system.

FIG. 4 is a plan view of a previously known 2-dimensional bulk beamsteering system.

FIG. 5 is a plan view of a single layer of active EO material andinsulator material to reduce fringing field effects.

FIG. 6 is a graph depicting step increments of two phase delayprogressions with a reset therebetween, using conductive electrodes.

FIG. 7 is a plan view of an embodiment having tilted electrodes andinsulators to reduce fringing field effects.

FIG. 8 is a graph depicting step increments of two phase delayprogressions with a reset therebetween, using resistive or tiltedelectrodes.

FIG. 9 is a plan view of a single layer of active EO material andinsulator material, having a reflective layer.

FIG. 10 is a plan view an embodiment having tilted electrodes andinsulators, having a reflective layer.

FIG. 11 is a schematic depiction of an EO active layer having a numberof active cells with discrete low-side electrodes.

FIG. 12 depicts an embodiment for a two-layer embodiment having a commonor continuous low-side electrode.

FIG. 13 depicts an embodiment for a four-layer embodiment having commonor continuous low-side electrodes.

FIG. 14 depicts an embodiment for a two-layer embodiment having a sharedcommon or continuous low-side electrode.

FIG. 15 depicts an embodiment for a four-layer embodiment having sharedcommon or continuous low-side electrodes.

FIG. 16 depicts a two-layer embodiment having a common or continuouslow-side electrode.

FIG. 17 depicts a two-layer embodiment having a shared common orcontinuous low-side electrode.

FIG. 18 depicts a single layer of active EO material having active cellswith varying thicknesses and a common or continuous low-side electrode.

FIG. 19 is a schematic diagram of a controller for steering an incidentEM beam.

FIG. 20 is a schematic diagram of another embodiment of a controller forproviding EM beam steering commands.

FIG. 21 is a schematic flow diagram of a procedure for steering incidentEM beams having distinct wavelength values.

FIG. 22 is a schematic flow diagram of a procedure for steering anincident EM beam in more than one axis or polarity.

FIG. 23 is a schematic flow diagram of a procedure for steering anincident EM beam.

FIG. 24 is a schematic flow diagram of a procedure for making and usingan EM beam steering device.

FIG. 25 is a schematic flow diagram of a procedure for operating an EMbeam steering device.

FIG. 26 is a schematic diagram of a beam steering device.

FIG. 27 depicts an embodiment of a single active layer of a beamsteering device.

FIG. 28 depicts another embodiment of a single active layer of a beamsteering device.

FIG. 29 is a schematic diagram of a controller for steering an incidentEM beam.

FIG. 30 is a graph depicting an example phase profile using a half-wavevoltage profile.

FIG. 31 is a schematic flow diagram of a procedure for operating an EMbeam steering device.

FIG. 32 is a schematic diagram of a beam steering device utilizing anelectro-optical crystal.

FIG. 33 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 34 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 33.

FIG. 35 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 36 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 35.

FIG. 37 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 38 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 37.

FIG. 39 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 40 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 39.

FIG. 41 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 42 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 41.

FIG. 43 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 44 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 43.

FIG. 45 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 46 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 45.

FIG. 47 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 48 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 47.

FIG. 49 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 50 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 49.

FIG. 51 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 52 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 51.

FIG. 53 is a schematic diagram depicting an alternate view of theembodiment presented in FIG. 51.

FIG. 54 is a schematic diagram of a varifocal lens.

FIG. 55 is a schematic diagram depicting a pair of varifocal lenses.

FIG. 56 is a schematic diagram of a beam steering device utilizing apair of varifocal lenses.

FIG. 57 is a schematic diagram of a beam steering device utilizing apair of varifocal lenses.

FIG. 58 is a schematic diagram of a beam steering device utilizing apair of varifocal lenses.

FIG. 59 is a schematic diagram of a beam steering device utilizing aconcave emission surface.

FIG. 60 is a schematic diagram of a beam steering device utilizing abulk crystal.

FIG. 61 is a schematic diagram of a beam steering device utilizing aconcave emission surface.

FIG. 62 is a schematic diagram of a beam steering device utilizing azero power meniscus lens.

FIG. 63 is a schematic diagram of a beam steering device utilizing azero power meniscus lens.

FIG. 64 is a schematic diagram of a beam steering device utilizing aconcave emission surface and a varifocal lens.

FIG. 65 is a schematic diagram of an example varifocal lens.

FIG. 66 is a depiction of illustrative performance of a beam steeringdevice utilizing a concave emission surface and a varifocal lens.

FIG. 67 is another depiction of illustrative performance of the beamsteering device utilizing a concave emission surface and a varifocallens.

FIG. 68 is a depiction of illustrative performance of a beam steeringdevice utilizing a concave emission surface.

FIG. 69 is a depiction of illustrative performance of the beam steeringdevice utilizing a concave emission surface and a varifocal lens.

FIG. 70 is a depiction of illustrative design or control characteristicsof a varifocal lens.

FIG. 71 is a depiction of illustrative design or control characteristicsof a varifocal lens.

FIG. 72 is a depiction of illustrative design or control characteristicsof a varifocal lens.

FIG. 73 is a depiction of illustrative design or control characteristicsof a varifocal lens.

FIG. 74 is a schematic diagram of a system for beam steering including aconcave emission surface and a varifocal lens.

FIG. 75 is a schematic block diagram of a beam steering controller.

FIG. 76 is a schematic block diagram of a varifocal lens controller.

FIG. 77 is a schematic block diagram of a beam steering controller.

FIG. 78 is a schematic flow diagram of a procedure for beam steering.

FIG. 79 is a schematic flow diagram of a procedure for applying aselected convergence amount to an incident electromagnetic beam.

FIG. 80 is a schematic flow diagram of a procedure for progressivelysteering an incident electromagnetic beam through steering portions of abulk steering crystal.

DETAILED DESCRIPTION

For the purposes of promoting an understanding of the principles of thedisclosure, reference will now be made to the embodiments illustrated inthe drawings and described in the following written specification. It isunderstood that no limitation to the scope of the disclosure is therebyintended. It is further understood that the present disclosure includesany alterations and modifications to the illustrated embodiments andincludes further applications of the principles disclosed herein aswould normally occur to one skilled in the art to which this disclosurepertains.

This disclosure relates to the field of optical beam steering and incertain embodiments includes modulo 2πn and bulk active layer beamsteering approaches, with a reduced number of moving parts, and/or nomoving parts. More particularly, this disclosure teaches a unique, new,diffraction-based beam steering device made of electro optical crystals,liquid crystals, quantum dot materials, or any other material whoseindex of refraction can be dynamically changed. Example devices willhave no moving parts. In certain embodiments, molecules in theelectro-active material move, such as in a nematic liquid crystal.

Steering an optical beam without moving parts requires the ability tochange the phase front exiting an optical device compared to the phasefront entering a device. The direction a beam is travelling can beperpendicular to the phase front of the beam. Traditionally, the phasefront of an optical beam, and the direction the beam is travelling, ischanged by moving a mirror, or a transparent optical element with anindex of refraction different from air. Two fundamental non-mechanicalmethods of creating a phase difference across an optical beam resultingin a steered optical beam are described herein. One method is to createan optical path delay (“OPD”), which is equivalent to a phase delay fora certain wavelength, and the other is to directly create a phase delay.An example disclosure of the direct phase approach is set forth in thepaper by S. Pancharatnam, in Proceedings of the Indian Academy ofSciences, vol XLI, no. 4, sec. A, 137, 1955. Some of the background forthis disclosure is discussed in “A review of phased array steering fornarrow-band electro-optical systems”, by Paul F McManamon, Philip J Bos,Michael J Escuti, Jason Heikenfeld, Steve Serati, Huikai Xie, Edward AWatson. The Pancharatnam paper, which may be referred to as “Reference1” hereinafter, discusses these technologies, and is incorporated hereinby reference in its entirety for all purposes.

Another example method to steer light without mechanical motion includeswriting a prism. Certain challenges with this approach include thedifficulty in creating an OPD as large as would be required to write afull prism of appreciable width. For example, a 10-cm wide aperturesteering to 30 degrees would require >5 cm OPD on the thick side of theprism. However, for a narrow wavelength, it is advantageous that lightis a sine wave.

With a sine wave it does not matter if there is a 0, 2π, 4π or 2nπ phaseshift. The unfolded phase profile is the same. Therefore, as one movesacross the width of the prism, an OPD can be created that subtracts 2πof phase, or one wavelength, every time the phase reaches 2π, resultingin a sawtooth OPD and a sawtooth phase profile. When the phase profileis unfolded, it is the same for the design wavelength as the profileresulting from light travelling through a prism. Unfolding the phasefront means adding the phase, or OPD, resets back into the prism. Resetsof any multiple of 2π, or any multiple of one wavelength, can be used.If resets are created perfectly, the unfolded phase at the designwavelength looks like the phase profile that would result frompropagation through a prism and steers light in the same manner as aphase shift resulting from light travelling through a prism.

A modulo 2π phase profile should be interpreted to mean a 2πn phaseprofile, with resets of any multiple of one wavelength of OPD. Discreteincrement modulo 2π beam steering is shown in FIG. 1. In the exampleshown in FIG. 1, discrete steps are used to build up to one wavelength(or a multiple of wavelengths, 2πn), or 2π phase shift. For example,discrete steps of 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, and330 degrees can be used, and then reset (e.g. at position 108) back to 0degrees instead of going to 360 degrees, because 0 degrees and 360degrees are the same in a sine wave. This is what would result fromindividual electrodes imposing an index change on a material, ignoringany fringing field effects. The benefit of using a modulo 2π phaseprofile is that the required OPD can be small, on the order of a singlewavelength (or a small multiple of the wavelength). In the example ofFIG. 1, a number of phase delay progression stages (e.g., group 102) areutilized to build up the 2πn phase shift, and a reset 108 is performedbetween each phase delay progression stage 102. The unfolded phaseprofile 104 is depicted, which is the equivalent phase shift of anincoming undisturbed phase front 106 (defined by the EM beam, andco-located with the position axis). It will be understood that anynumber of phase delay progression stages 102 may be utilized, eachhaving any number of discrete steps to build them. Additionally, phasedelay progression stages 102 may not be discrete, but may be continuousor partially continuous as described throughout the present disclosure.

Additionally, each phase delay progression stage 102 may be distinctfrom one or more of the other phase delay progression stages 102, forexample where a first stage 102 provides a 2π phase shift, and where asecond stage 102 provides a 4π phase shift (e.g., utilizing twice thedistance along the position axis, thereby providing the designedunfolded phase profile 104). Additionally or alternatively, phase delayprogression stages 102 need not be in the same plane—for example wherethe incident EM beam encounters one of the phase delay progressionstages 102 on a first plane, and a second one of the phase delayprogression stages 102 on a second plane (e.g., reference FIG. 12).

For Modulo 2πn beam steering the maximum required OPD (i.e., the minimumthickness of the electro-optic (EO) material at the maximum phase shiftlocation) is approximately equal to the wavelength of the light beingsteered. In certain embodiments, a thicker EO material may be utilized,such as a multiple of the wavelength of light being steered. The modulo2π steering approach makes the beam steerer subject to wavelengthdependence, or dispersion. The wavelength dependence results in varyingwavelengths steered to varying angles. This wavelength dependence isdiscussed in: P. F. McManamon, E. A. Watson, T. A. Dorschner, L. J.Barnes, “Nonmechanical beam steering for active and passive sensors,”SPIE 1417, 110, 1991, p 194. The McManamon paper “Nonmechanical beamsteering . . . ”, which may be referred to as “Reference 2” hereinafter,is incorporated herein by reference in its entirety for all purposes.The wavelength dependence is further discussed in: P. F. McManamon, J.Shi, and P. Bos, “Broadband optical phased-array beam steering,” Opt.Eng. 44, 128004, 2005. The McManamon paper “Broadband opticalphased-array beam steering”, which may be referred to as “Reference 3”hereinafter, is incorporated herein by reference in its entirety for allpurposes.

Wherever a wavelength is recited (e.g., of light, EM radiation, and/oran optical or photonic beam) and/or where λ is recited, throughout thepresent disclosure, it will be understood that the wavelength (or λ) maybe a nominal wavelength, a particular wavelength, and/or an effectivewavelength. For example, a nominal wavelength may be the wavelength of atarget or considered EM radiation frequency in a vacuum, in air, orunder selected conditions. In another example, a particular wavelengthmay be a wavelength of a target or considered EM radiation frequency atspecific conditions, such as through an EO active material at a selectedvoltage value (e.g., thereby at a selected refractive index for thatfrequency of EM radiation). In another example, an effective wavelengthmay be the in-situ wavelength of the EM radiation frequency in the EOactive material, an average of certain values (e.g., an average of thehigh- and low-phase delayed values in a given active cell, etc.), and/orone or more active cells may be configured for distinct λ values, evenfor a particular frequency of EM radiation (e.g., depending upon thecurrent, expected, or designed optical conditions for the one or moreactive cells). Accordingly, λ should be understood throughout thepresent disclosure to indicate any of these usages. One of skill in theart, having the benefit of the present disclosure and informationordinarily available when contemplating a particular system and/or anaspect of the system, can readily determine which usage of λ is relevantfor the particular system and/or the aspect of the system. Certainconsiderations for determining which one or more usage of λ applies to aparticular system or aspect of the system include, without limitation:the optical characteristics of the EO active material(s) of the system;the phase delay progression planned for the system; the voltage profileand/or optical characteristic profile of the system; the efficiencyconsiderations for the system including the cost of power, the risksrelated to side lobes, and/or the costs associated with undesiredthermal generation in relevant parts of the system; the duty cycle ofoperating conditions (e.g., power throughput, steering directions andmagnitudes, and/or on-time); and/or the steering capability (e.g.,degree of steering, number of axes of steering, and/or number ofpolarities of steering) to be supported by the system.

An important parameter for beam steering is steering efficiency. As usedherein, the term steering efficiency should be understood broadly.Various options and configurations described throughout the presentdisclosure affect different aspects of the steering efficiency, andaccordingly it will be understood by one of skill in the art, having thebenefit of the present disclosure, how to determine which aspects of thepresent disclosure are important to varying embodiments. Withoutlimitation, steering efficiency can be understood to include energytransport considerations, cost considerations, risk considerations,and/or capability considerations. Without limitation, steeringefficiency can be understood to be any one or more of the following: theamount of incident energy of the EM on the beam steering device thatreaches the targeted location; the similarity of the phase profile ofthe steered EM beam on reach the target relative to the incident EM beamand/or relative to an idealized prism; the amount of energy of theincident EM beam that does not reach the target location (e.g., sidelobes and/or heating losses); the amount of energy of the incident EMbeam that creates an undesirable effect (e.g., a concentrated sidelobe); the amount of energy of the incident EM beam that dissipates asheat and/or where the heat is dissipated; the number of electro-optical(EO) layers utilized to achieve a given steering capability; the cost ofmanufacture (e.g., materials, fabrication, testing, etc.) for aparticular design; the opportunity cost of a lower system capability(e.g., steering amount, wavelengths supported, profile consistency,etc.); the capital and/or operating cost of a higher system capability;and/or the risk cost of a particular steering device (e.g., due to sidelobes and/or the particular arrangements of the side lobes, wavelengthselections which may have varying risks, and/or system reliability orpower consumption which may put certain applications at risk).

Certain considerations to determine which steering efficiency factorsare important for a particular application include, without limitation:the utilization environment for the beam steering device includingrobustness to side lobes; EM wavelength values to be utilized; capitalcost sensitivity; operating cost sensitivity; costs and availability ofpower for the beam steering device in use; costs and availability ofcomputing power for the beam steering device in use; costs,availability, and capability for manufacturing including materials andfabrication; the critical mission aspects for a particular applicationsuch as targeting capability, response time, and similarity of phaseprofile requirements; and/or the sensitivity of parts of the beamsteering device and/or the utilization environment to heating and/orside lobe energy from beam steering operations. One of skill in the art,having the benefit of the disclosure herein and information ordinarilyavailable when contemplating a particular system, can readily determinewhich factors of steering efficiency determinations are important to aparticular embodiment, and further which features of systems and/ortechniques described throughout the present disclosure relate to thosefactors of steering efficiency. The foregoing sets forth an example ofcertain considerations for certain systems, and any other considerationsset forth throughout the present disclosure may also be utilized inconfiguring a particular embodiment of the present disclosure.

The terms optical light, optical, EM radiation, EM beam, light, photonicbeam, and other similar terms as used throughout the present disclosureshould be understood broadly. The present disclosure contemplatessteering EM radiation of any type depending upon the application and theavailable materials. In certain embodiments, EM radiation as utilizedherein contemplates optical light, or light that is within the visiblespectrum. In certain embodiments, optical light additionally includes atleast a portion of the ultra-violet spectrum, and/or at least a portionof the infra-red spectrum. In certain embodiments, optical light and/orEM radiation includes one or more contemplated wavelengths and/orportions of the EM spectrum, and does not include portions of the EMspectrum that may otherwise be considered “optical light” outside thecontext of the particular system. It will be understood that variouselectro-magnetic wavelengths of interest are contemplated herein,including wavelengths that are not visible, and/or are not typicallydescribed as optical wavelengths or “light.” Without limitation, theterms optical and light, as used herein, include at least infrared,visible, and ultra-violet frequencies, and in certain embodiments mayinclude frequencies of the electromagnetic spectrum that are outsidethese ranges. One of skill in the art, having the benefit of the presentdisclosure and information ordinarily available when contemplating aparticular system, can readily determine the EM radiation, opticallight, light, and/or EM beam parameters for the system. Certainconsiderations when determining the EM radiation, optical light, light,and/or EM beam parameters for a system include, without limitation: theavailable materials for fabricating EO layers, substrates, reflectivematerials, and/or electrodes; the transmissivity and/or optical changecharacteristics for materials at frequencies of interest; the EMfrequency requirements for an application (e.g., eye safety, resolutionrequirements, and/or available EM sources); and/or the availablethickness of materials as fabricated (e.g., limiting the steerablewavelengths of EM radiation such as at longer wavelengths).

One issue with any modulo 2π beam steering system that affects thesteering efficiency is “fly-back,” which refers to the spatial distancerequired to reduce the OPD by a 2πn wavelength (e.g., a “reset”, such asfrom approximately a multiple of one wavelength, or 2πn phase shift, tonear zero). Reducing the OPD from that which results in a 2πn phaseshift to zero means from approximately 2πn to approximately zero. Thereare various embodiments and techniques for specifying the exact OPDlevel from which a reset subtracts OPD. While each of these techniquesreduce the OPD by 2πn in phase for the design wavelength, they do notall start at exactly an OPD that is equivalent to a 2πn phase shift, butcan start at somewhat higher or lower values that are close to 2πn, andcan end at values that are somewhat higher or lower than zero. Forexample, referencing FIG. 2, a phase shift curve 200 depicts an examplereset portion 202. An ideal reset 202 would show the phase shift curve200 dropping vertically from a phase shift profile that followed anideal prism profile to a value shifted by 2πn to the selected resetstate (which may be a non-zero voltage value), and the progressing againat an ideal prism angle in the next stage. However, previously knownmodulo 2π beam steering system have a significant fly-back effect asdepicted in FIG. 2, where the pre-reset profile falls off of the idealprism profile before reaching the reset portion, and does not fall allthe way to the designed reset value before returning to the prism curve.The fly-back effect causes a loss of steering efficiency, where aportion of the incident EM beam is not steered to the desired location,and further can cause heating, side lobes, or other undesired effects asthe improperly steered energy of the EM beam is dissipated in anotherportion of the system or the environment.

The example of FIG. 1 depicts an idealized modulo 2πn system having nofly-back effect, while the example of FIG. 2 depicts an examplepreviously known modulo 2πn system having a nominal fly-back effect.Various features throughout the present disclosure have been found togreatly reduce the fly-back effect, including without limitation theutilization of insulators, vertical spatial changes between adjacentphase delay progression stages (e.g., reference FIG. 12 and FIG. 18),enhanced insulation at reset positions, and/or control or modulation ofelectrodes. In certain embodiments, systems and/or methods forperforming modulo 2πn beam steering described throughout the presentdisclosure can approximate the unfolded phase profile 104 depicted inFIG. 1.

FIG. 6 is an example depiction of a realistic phase profile 602 which,according to modeling and calculations, it is believed to be achievableusing various aspects of the present disclosure. The example of FIG. 6utilizes conductive electrodes. The representation of FIG. 6 isnon-limiting: certain systems may have a less ideal phase profile 602than that depicted in FIG. 6 and nevertheless realize certain benefitsof the present disclosure, and certain systems may have a more idealphase profile 602 than that depicted in FIG. 6, such as by combiningaspects of the present disclosure, utilizing higher capabilitymaterials, more elaborate configurations of electrodes, controllableelectrodes, tilted or contoured electrodes, and/or by increasing thenumber of steps in one or more of the phase delay progressions.

FIG. 8 is an example depiction of a realistic phase profile 802 which,according to modeling and calculations, it is believed to be achievableusing various aspects of the present disclosure. The example of FIG. 8utilizes resistive electrodes. The representation of FIG. 8 isnon-limiting: certain systems may have a less ideal phase profile 802than that depicted in FIG. 8 and nevertheless realize certain benefitsof the present disclosure, and certain systems may have a more idealphase profile 802 than that depicted in FIG. 8, such as by combiningaspects of the present disclosure, utilizing higher capabilitymaterials, more elaborate configurations of electrodes, controllableelectrodes, tilted or contoured electrodes, and/or by increasing thenumber of steps in one or more of the phase delay progressions.

Disclosed herein are example modulo 2πn active material steeringapproaches, where a modulo 2πn active material will be from sub-micronlevel thickness to many tens, or even hundreds, of microns thick.Certain example modulo 2πn active material beam steering approachestaught use resets to limit the thickness of the active layer. An exampleembodiment utilizes an active single layer with thin insulators betweenelectrodes going through the active material. Certain features describedherein enhance efficiency throughput, such as, use of an insulator, anoptically active material, and/or a substrate transparent to theincoming light and/or having respective refractive indexes in aconfigured manner, such as refractive indexes that are similar. Theinsulators between the electrodes may, or may not, be all the waythrough the active layer. In certain embodiments, insulators may not betransparent to the incoming light.

The term transparent, as used herein, should be understood broadly, andincludes at least materials that allow transmission of electromagneticradiation of selected wavelengths: to a selected degree, virtuallycompletely, above a threshold level, and/or sufficiently to perform theunderlying task. The amount of transmission that is transparent, forexample sufficient to perform the underlying task, will be understood toone of skill in the art having the benefit of the present disclosure.Without limitation, certain considerations to determine an amount oftransmission that is transparent include: the cost and availability ofmanufacturing materials; the cost of fabricating a given device; theutilization of the device including required resolutions, detectionthresholds, and the like; the criticality of the device relative to asystem or application of the device; heat dissipation constraints and/orconsiderations of the device; and/or the availability of processingresources to enhance the capability of the device in the presence ofreduced transmission of EM radiation through the transparent componentsof the device. A transmission level that is transparent for oneembodiment in the full context of a particular device or system may beconsidered not transparent in the full context of another device orsystem—for example a same insulator component that is transparent forone device may be reflective or not transparent in the context ofanother device.

In certain embodiments, materials are described throughout the presentdisclosure as having a close optical value or characteristic (and/or asimilar optical value or characteristic), such as birefringence and/oran index of refraction. Optical values that are close depend upon thespecific system. In certain embodiments, optical values that provide forsufficient transmission of light therethrough, and that do not disturbthe EM beam such that a target steering capability and/or steeringefficiency can be met are within the scope of close optical values asunderstood herein. In certain embodiments, EO active materials havevarying optical characteristics, while insulators, substrate, and/orelectrode materials have non-varying (or not intentionally varied)optical characteristics, and thereby a static optical characteristic isbeing matched (“close”) with a varying optical characteristic. Incertain embodiments, the static optical value is selected to be a valuebetween the ranges of the varied optical characteristic. In certainembodiments, the static optical value is selected to be a value near amore important portion of the varying optical characteristic range, forexample close to the unsteered value, close to a maximum steering value,and/or close to a frequently occurring steering value. In certainembodiments, a static optical value may be outside of the range of thevaried optical characteristic and nevertheless be close to the variedoptical characteristic as contemplated herein. In certain embodiments,materials may be considered to have close or similar opticalcharacteristics at EM frequencies of interest, even if they do not haveclose or similar optical characteristics away from EM frequencies ofinterest. In certain embodiments, as described throughout the presentdisclosure, anti-reflective materials may be utilized in addition to, oras a replacement for, the utilization of materials having closelymatched optical characteristics. Example and non-limiting ranges formaterials having a close optical characteristic include: materials whichare the same (e.g., although one may have variance applied as an EOmaterial), and/or materials which have a selected optical property at aselected wavelength or range of wavelengths (e.g., index of refractionat 9.4 μm) within a specified range (e.g., sufficient to supportsteering efficiency targets) at a specified condition (e.g., duringselected steering operations). One of skill in the art, having thebenefit of the present disclosure and information ordinarily availablewhen contemplating a particular system, can readily determine materialshaving a close optical characteristic for the system. Certainconsiderations for determining whether materials have a close opticalcharacteristic include, without limitation: the cost and availability ofsuitable materials (including material cost and/or fabricationconsiderations); the frequency(ies) of interest of steered EM beams; thetarget steering efficiency values; the target steering capability; theduty cycle of steering for the application (e.g., the range of steeringvalues expected, and/or the time or power throughput at each steeringvalue); and/or the availability of mitigating techniques for the systemto compensate for optical differences (e.g., electrode configurations torecover steering efficiency, number of layers of active elements, thethickness of active and inactive elements, and/or utilization of“chess”, “castle”, or other configurations).

One design consideration is the thinness of the insulators between theactive material. Thicker insulators generally provide for improvedisolation between phase delay progression stages, and reduce fly-back atthe reset position. Thinner insulators generally provide for enhancedactive fill. Depending upon the materials for the active material, theinsulator, and the substrate, either thinner or thicker insulators mayincrease the overall cost of the beam steering device, including effectson material costs and/or fabrication costs.

In certain embodiments, the ground (or low-side) electrode may becontinuous (e.g., reference FIG. 9, 10, or 12), and can be eitherreflective, or transparent to the incoming light. In certainembodiments, the electrically hot electrodes (or high-side) arediscrete. In certain embodiments, the electrically hot electrodes aretransparent to the incoming light. Alternately or additionally, one ormore discrete electrodes could be embedded with, or behind, a reflectivelayer. In certain embodiments, the discrete electrodes are conductive.

An example second embodiment includes discrete electrodes that areresistive. Certain embodiments reduce the fringing field effect. Anembodiment which has conductive electrodes, at least without furtheradjustments as described herein, will in general suffer from thequantization loss. In certain embodiments, the utilization of tiltedand/or profiled electrodes can reduce or eliminate quantization losses,with or without the use of resistive electrodes. In certain embodiments,resistive electrodes can reduce or eliminate quantization losses. Incertain embodiments, combinations of tilted and/or profiled electrodeswith conductive and/or resistive electrodes may be utilized to supportreduction or elimination of quantization losses, other system lossessuch as electrical losses, and/or to support various fabricationtechniques. In an example embodiment having resistive electrodes, twovoltages are applied to the resistive electrode, resulting in a tilted(or progressive) electric field, and a tilted (or progressive) indexchange. Example embodiments having resistive electrodes reducequantization loss, for example by achieving a phase delay progressionstage 102 with fewer electrodes, or even with a single electrode. Incertain embodiments, two or more voltages are applied at selectedlocations across the electrode (e.g., using solid state deviceselectrically coupled to various positions of an electrode). The use ofmultiple voltages can achieve a non-linear slope of the voltages, forexample to achieve a linear OPD change across the EO material or to beresponsive to a non-linear electrode resistivity profile.

Another example embodiment includes at least two optically active rows630 interposed between two substrates 600, 605, as shown in FIG. 12. Theexample of FIG. 12 utilizes two, or a multiple of two, layers,alternating a transparent insulator with a transparent active layer,providing a 100% fill factor (or arbitrarily close to 100%, if desired)of active electro-optic (EO) material capable of causing an OPD changein the radiation. The example of FIG. 12 or similar arrangements can beutilized to avoid the profile gaps in the unfolded phase profile such asdepicted in FIG. 6 or 8, which contribute to steering efficiency losses(e.g., by having an increased active layer fill factor). The example ofFIG. 13 depicts a multiple of two layers, although any number of layersmay be utilized. It will be understood that where an incident EM beamhas portions that intersect a different number of layers (e.g., anembodiment having an odd number of active layers with alternating cells,where a first portion intersects two active layers and a second portionintersects three active layers), the OPD in one or more layers may bemanipulated (e.g., using varying voltages and/or electrodeconfigurations) to ensure that all steered portions of the incident EMbeam are steered to the same degree. An example of FIG. 12 may utilizeconductive electrodes or resistive electrodes. The example of FIG. 12has reduced loss due to fringing fields.

A further example embodiment includes resistive electrodes and two, ormore, voltages on one side (and/or a voltage progression), to reduce, oreliminate the quantization loss. The further example embodiment includesan effective 100% fill factor, negligible fringing field loss, andnegligible quantization loss. For example, referencing FIGS. 12 and 13,the utilization of resistive electrodes can reduce or eliminatequantization losses in the active cells. The example of FIG. 13 shows 4device layers, but in certain embodiments more device layers could beused.

The example of FIG. 7 shows tilted electrodes 50. Tilted electrodes 50can have a similar effect as resistive electrodes by creating a voltagevariance across the active cell. In certain embodiments, the tiltedelectrodes 50 may be more difficult to fabricate, and the amount of tiltof the tilted electrodes 50 may not be adjustable at run-time. However,in certain embodiments, constructing the tilted electrodes 50 mayprovide for a field variance that more reliably achieves a designvariance than a resistive electrode embodiment, and/or that provides forimproved operation as wear and aging affect the resistance profile ofthe electrodes. Additionally or alternatively, example embodimentsinclude adjustments to the tilted electrodes 50, such as providing morethan one tilted electrode 50 per active cell, where selection of anactive one of the tilted electrodes 50 provides for run-time adjustmentof the electric field. The tilted electrodes 50 are depicted as a lineartilt, but the progression of the electrode and the spacing between thehigh-side electrode and the low-side electrode may be any shape, forexample to account for a non-linear EO active material response and/or anon-linear resistance in the electrodes. In certain embodiments, givenactive cells may include tilted electrodes 50 and/or resistiveelectrodes. In certain embodiments, a first active cell may have a firsttilted electrode 50 and/or resistive electrode configuration, and asecond active cell may have a second tilted electrode 50 and/orresistive electrode configuration. In certain embodiments, theutilization of tilted electrodes 50 can produce a phase profile 802similar to that depicted in FIG. 8.

The example of FIG. 7 depicts the tilted electrode 50 progressingthrough the EO active material 10 at a selected trajectory. It will beunderstood that the tilted electrode 50 can be on a first side of the EOactive material 10, for example with a shaped active cell rather thanhaving the tilted electrode 50 traverse through the EO active material10. The example of FIG. 7 depicts insulators 20 between active cells ata reset position, which may be configured as any insulator describedthroughout the present disclosure, including fully dividing activecells, partially dividing active cells, and/or the insulators 20 being apart of a substrate (not shown in FIG. 7). The example of FIG. 7 depictsa common ground electrode 40, although any ground electrodeconfiguration described throughout the present disclosure may beutilized with tilted electrodes 50.

Yet another example embodiment includes at least two optically activerows separated by a continuous ground electrode, for example consistentwith the depiction in FIG. 14 for two optically active rows, and in FIG.15 for more than 2 optically active rows. Example embodiments includeeach active layer having an array of active cells. In the examples, anactive cell is the EO active material positioned between the continuousground electrode and a discrete electrode, and an insulator cell ispositioned between each two active cells.

Referencing FIG. 11, an EO active layer 3 is positioned between a row ofdiscrete low-side electrodes 4 and a corresponding row of discretehigh-side electrodes 2, and positioned within a substrate 1. The exampleof FIG. 11 utilizes the EO active material as an insulating gap betweenactive cells and the substrate 1 as an insulating gap between high-sideelectrodes, where the active cells are the EO active layer 3 portionsbetween the electrode pairs 4,2. It can be seen that the embodiment ofFIG. 11, while not necessarily depicted to scale, may have a relativelylow active fill factor, where a significant fraction of the incident EMbeam does not pass through an active cell. In certain embodiments, thesteering efficiency losses in an embodiment such as depicted in FIG. 11are nevertheless acceptable. In certain embodiments, an embodiment suchas depicted in FIG. 11 may additionally include another steering layerhaving an EO active material, high-side electrodes, and low-sideelectrodes (which may be shared with a different steering layer). Thehigh-side electrodes 2 in FIG. 11 may be conductive or resistive. Incertain embodiments, a configuration such as that depicted in FIG. 11 isnot sufficiently capable to provide EM beam steering with acceptablesteering efficiency for certain applications.

Referencing FIG. 12, an example beam steering device includes a numberof active cells 630, each positioned between a discrete high-sideelectrode 660 and a low-side electrode 650, 670. The low-side electrode650, 670 in the example of FIG. 12 is a common ground electrode, withone common ground electrode 650, 670 for each active layer 610, 620. Inthe example of FIG. 12, an upper substrate 600 and lower substrate 605are provided, which may structurally define the beam steering device. Incertain embodiments, one of the substrates 600, 605 may be reflectiveand/or include a reflective layer. In certain embodiments, groundelectrode 670 may be reflective and/or include a reflective layer. Theexample beam steering device further includes a number of insulators640, the insulators 640 positioned between each adjacent active cell630. The insulators 640 may be a transparent material, and/or may havean optical characteristic that is close to the optical characteristic ofthe active cells 630. In certain embodiments, the insulators 640 may beair. In certain embodiments, the active cells 630 are arranged to applya progressive phase delay to an incident EM beam, for example within acell 630 (e.g., utilizing a resistive electrode or other aspect to applya voltage gradient across the cell), and/or across several of the activecells 630, with the active cells 630 forming phase delay progressionstages. It can be seen that a phase delay progression may begin with anactive cell 630 in a first active layer 610, and continue with an activecell 630 in the second active layer 620. In the example of FIG. 12,resets may occur at each active cell 630 (e.g., a next cell resets thephase delay by 2πn), or between adjacent cells 630 at the boundaryseveral active cells 630 forming phase delay progression stages. Incertain embodiments, both the geometry of the active cells 630 creatingdistance between the high-side electrodes 660, and the insulators 640 ofthe beam steering device, cooperate to provide for sharp resets thathave greatly reduced fly-back effect and subsequent steering efficiencylosses.

Referencing FIG. 13, an example beam steering device is depicted havinga number of active layers 680, 685, 690, 695. Each active layer 680,685, 690, 695 includes active cells 740 including an EO active materialpositioned between a discrete high-side electrode 760 and a low-sideelectrode. The low-side electrodes 730 in the example of FIG. 13 arecommon ground electrodes, with one common ground electrode provided foreach active layer 680, 685, 690, 695. The example beam steering devicefurther includes substrates 710, 720, and insulators 750. The examplebeam steering device of FIG. 13 depicts multiple stacked active layers680, 685, 690, 695, allowing for greater steering capability and/orgreater steering efficiency of the device.

Referencing FIG. 14, an example beam steering device is depicted havingtwo active layers 770, 775. Each active layer 770, 775 includes activecells 790 including an EO active material positioned between a discretehigh-side electrode 810 and a low-side electrode. The low-side electrode1402 in the example of FIG. 14 is a common ground electrode, with twoactive layers 770, 775 sharing the common ground electrode. The examplebeam steering device includes a first substrate 805 on an incident sideof the beam steering device, and a reflective layer 820 on the opposingside of the beam steering device. The use of a reflective layer 820provides for additional steering capability, essentially doubling theeffective steering capability of the active layers 770, 775.

Referencing FIG. 15, an example beam steering device is depicted havingfour active layers 830, 840, 850, 860. Each active layer 830, 840, 850,860 includes active cells 790 including an EO active material positionedbetween a discrete high-side electrode 810 and a low-side electrode. Thelow-side electrodes 1502, 1504 in the example of FIG. 15 are commonground electrodes, with two active layers (830, 840 and 850, 860,respectively) each sharing the common ground electrode. The example beamsteering device includes a first substrate 870 on an incident side ofthe beam steering device, and a reflective layer 890 on a secondsubstrate 875 on the opposing side of the beam steering device.

Yet another example embodiment includes at least two optically activerows (or active layers) separated by a continuous ground electrode,having resistive high-side electrodes and two, or more, voltages (and/orvoltage gradients) provided across the active cells. Certain embodimentshaving at least two optically active rows separated by a continuousground electrode have an effective 100% fill factor (e.g., the amount ofthe incident EM beam that is directed into active cells in at least oneof the active layers), and/or an effective fill factor that isarbitrarily close to 100%, including greater than 90%, greater than 95%,greater than 97%, or greater than 99%. In certain embodiments,negligible fringing field loss and/or negligible quantization loss. Incertain embodiments, there are even number of active rows, each activerow including an array of active cells with an insulator cell locatedbetween each two active cells. Additionally or alternatively, an oddnumber of rows may be present in certain embodiments as will beunderstood by one of skill in the art having the benefit of the presentdisclosure. An example embodiment includes the positions of active cellsand insulator cells in the neighboring rows that are opposite. Incertain embodiments, the size and position of each active cell isselected in response to the size of the corresponding insulator cell inthe next row—for example sized the same and aligned. In certainembodiments, active cells within a layer, and/or active cells indistinct layers, may be varied in size and/or thickness.

In certain embodiments, the active cells, thickness of active cells,electrodes, and applied voltages, are configured such that an incidentEM beam of a selected wavelength (or frequency) experiences an identicalor a sufficiently similar (e.g., consistent with the designed steeringefficiency for the beam steering device) phase delay progression acrossthe area of the EM beam such that the EM beam is steered to a desireddegree at the selected steering efficiency. In certain embodiments, theactive cells, thickness of active cells, electrodes, and appliedvoltages, are configured such that the steered portions of the EM beam(e.g., not the portions lost to an effective fill factor less than 100%)experience the identical or the sufficiently similar (e.g., consistentwith the designed steering efficiency for the beam steering device)phase delay progression across the area of the EM beam. In certainembodiments, the active cells, thickness of active cells, electrodes,and applied voltages, are configured such that an incident EM beam ofone of a number of selected wavelengths (or frequencies), and/or steeredportions of such incident EM beams, experience an identical or asufficiently similar (e.g., consistent with the designed steeringefficiency for the beam steering device) phase delay progression at eachof the selected frequencies. For example, and without limitation, anexample beam steering device includes one or more active layersconfigured to steer a first selected frequency and to be transparent (orsufficiently transparent) to other selected frequencies, and furtherincludes one or more other active layers configured to steer a secondselected frequency and to be transparent (or sufficiently transparent)to the first selected frequency. In certain embodiments, an active layercan be configured to steer more than one frequency—for example where thesteered frequencies are multiples of a same wavelength, such as when athickness of an active cell is the same as a higher wavelength, anddouble (for example) the thickness of a lower wavelength.

In certain embodiments throughout the present disclosure, active cellsin adjacent layers are offset (e.g., reference FIGS. 12-15) from eachother in an alternating pattern. For the purpose of the presentdisclosure, such arrangements may be referenced as a Chess Scanner or aChess Pattern. Certain embodiments having resistive discrete high-sideelectrodes and a Chess Pattern arrangement may be referenced as a ChessScanner Pro (or a Chess Pattern Pro). The embodiments of FIGS. 12 to 15depict two active layers cooperating to provide the effective fill areaof the beam steering device in the Chess Pattern, but it will beunderstood that three or more layers, and/or randomized orpseudo-randomized layers can be arranged to provide the effective fillarea of the beam steering device. The terminology of Chess Scanner orChess Scanner Pro embodiments is used for convenience and clarity of thedescription herein. It will be understood that, in certain embodiments,the sizing, alignment, and/or arrangement of cells may vary such thatthe arrangement of the active cells and the insulator cells do notresemble a chess board. Without limitation, variance of sizing,alignment, and/or arrangement may include less than complete coverage ofthe optical area with cells, oblique, curved, or other non-perpendiculararrangements of cells, and/or cells having non-square shapes and/orvarying shapes and sizes.

In certain embodiments, the substrates, active material, and/orinsulators are transparent to the incoming optical wave to be deflectedby the scanner, and/or have a similar refractive index between the twomaterials. It will be understood that transparency and/or refractiveindex similarity may improve the throughput of the device. In certainembodiments, materials may be non-transparent, transparent at selectedwavelengths, and the like. An example embodiment includes an optionalreflective layer added, which may be the last layer of the scanner(and/or the last optically active layer of the scanner). The reflectivelayer may be the last layer, and/or may be after a transparent lastlayer of the beam steering device. In certain embodiments, thecontinuous ground electrode in certain embodiments, and/or the lastground electrode in certain embodiments, may be reflective. Theinclusion of a reflective layer causes the optical wave to traverse thescanner a second time, effectively doubling the thickness of the activelayers, and increasing the steering capability and/or steeringefficiency.

Each optically active row contains a series of cells made of an electrooptically active material, such as an EO crystal (which could be KTN,PMN-PT, BaTIO₃, SBN, or some other crystal material), a quantum dotmaterial, a liquid crystal, and/or any other optically active material.In certain embodiments, distinct layers and/or distinct cells within alayer may include distinct materials from other layers or cell in adevice. Each material whose index of refraction can be changeddynamically is sandwiched between two electrode layers. One layer can beground, and one layer can apply a voltage other than ground.Alternately, both layers can apply a voltage different from zero. Incertain embodiments it may be advantageous to use more than a singleactive material type.

Example electrodes are transparent to an incoming wave and can be eitherconductive, using only one applied voltage, or resistive using two ormore applied voltages, while creating a linear, or non-linear, voltageramp between the location where the two voltages are applied. Theresistive layer will provide a varying voltage, from the lowest to thehighest voltage applied to the electrode. In certain embodiments,portions of the high-side electrode may be resistive, and other portionsof the high-side electrode may be conductive. In certain embodiments,the resistance of the high-side electrodes may be controllable—forexample with multiple resistive elements provided across the high-sideelectrode, where a controller can configure the resistive arrangementduring operations of the beam steering device. In a further example,solid state switches, Zener diodes, OP Amps, and/or other solid statedevices may be used to provide suitable control of the high-sideelectrode resistances with a response time configured to meet thefunctions of the beam steering device.

In certain embodiments, the electrodes are fabricated from transparentconductor materials, such as In—Sn oxide or and In—Sn alloy. If areflective layer is used on one side, then that side could be made witha conductor that is not transparent to optical radiation. The level ofconductivity can be any of a wide variety of levels. A ground (orlow-side) electrode can be continuous or discrete, but the high-sideelectrodes imposing spatially varying voltage are discrete and/orseparated by insulator cells and/or geometric spacing providing aninsulating function. In certain embodiments, insulator cells are made ofthe same material as the substrate, or some other material with asimilar index of refraction as the substrate. As an alternative theinsulator material could be air.

In certain embodiments, the refractive indices of the substrate, activematerial, and/or insulator have similar optical properties, and/or ananti-reflective coating can be used where material discontinuity occurs.The utilization of similar optical properties in materials can improvethe throughput of the beam steering device. Using anti-reflectioncoatings can improve steering efficiency. In certain embodiments, aninsulator cell is positioned between each of the optically active cells.In one embodiment, the arrangement of EO cells and insulators arereversed in each row. In certain embodiments, the active cells, whoseindex of refraction can be electronically modified, have the same sizeas the corresponding insulators in the next row. Alternately multipleactive cells could be used, such that sum of the width of the cells isthe same as the width of an insulator. In certain embodiments, theinsulators, and substrate, are made of the same material, such SrTiO3 orinfra-red glass to not only separate electrodes under different voltagesbut also to transmit the incoming EM wave. As an alternative one ormore, or all, of the insulators may be air. In certain embodiments, thetransparent insulator and active region above or below are the samesize, and the next pair of insulator/active region materials are adistinct size.

For improved throughput the refractive indices of substrate, active andinsulator cells should be close, and/or an anti-reflective coating canbe used on any edges where material discontinuity occurs to improvesteering efficiency. An ideal steering device would re-direct 100% ofthe impinging light. In one embodiment a high efficiency beam steeringmay redirect >90% of the light impinging on a device to exit at thesteered angle. Various beam steering applications can make use ofdifferent levels of steering efficiency. In one embodiment, the opticalwaves can be in the visible through long wave infrared. In oneembodiment, the surface figure of the substrate, insulators andelectrodes should be at least 1/50 of the wavelength of the incomingwave which in a UV, optical, or infrared, embodiment can be a wavelengthof 0.25 to 12 microns. In certain embodiments, the optically activecells provide at least approximately one wavelength of phase delay, andthus have a depth or layer thickness of at least one wavelength dividedby the index change ratio. In certain embodiments, a beam steeringdevice having a reflective layer includes optically active cellsproviding at least approximately one-half wavelength of phase delay, andthus have a depth or layer thickness of at least one-half wavelengthdivided by the index change ratio. In certain embodiments, the thicknessof the optically active cells progresses with the phase change delay,and/or may further include features to ensure that steering occurs in asingle direction across the array of active cells (e.g., throughmechanical control of the array facing, and/or control of the incidentEM beam where such control is possible). The width of each active cellcan be selected to adjust the deflection angle of the scanner, andfurther depends upon the phase delay progression scheme of a particularbeam steering device.

In one embodiment, if the scanner is designed to steer a wave with1.5-micron wavelength light to an angle of up to 30 degrees, the widthof each EO cell (or active cell) would be 3 microns or less. If EO cellsare of varying sizes then the largest cell will have a width of 3microns. In the example, the size of insulator cells, which are betweenevery two EO cells, are the same as the corresponding active cells inthe next row.

An example includes the second optically active row of the scanner thatis similar to the first row with the exception that the positions of theactive, and insulator cells, are opposite. The alignment of electrodesand insulators in the two rows are very important to provide an optimumphase delay for the whole incoming wave. After an incoming optical orphotonic wave traverses both layers the complete wave will haveexperienced a phase delay with discrete phase shifts based on the totalshift of the two layers. Layer 1 will shift the optical or photonic wavein its active regions, then where layer 1 has an insulator, layer 2 willshift the wave in its active regions, and the shift will continue inthis manner across the beam steering device.

Those active index changing layers that use a resistor, instead of aconductor, can vary the voltage across the active cell in a manner tomatch the waveform tilt resulting from the imposition of a series ofdiscrete index change steps. In this manner, quantization loss, asexplained in References 1 and 2, can be reduced or eliminated andapproximately one wavelength of OPD can be provided in a singleresistive electrode width, to deflect the incoming light to the maximumangle.

In one embodiment, each of the electrode layers can have thousands ofdiscrete electrodes in one row, and each phase reset can contain one ormore electrodes. Larger deflection angles require fewer electrodes of acertain width between resets, because the spatial period between resetsis smaller. In the case of resistive electrodes, the reset period can beas small as one resistive electrode width. In case of having conductiveelectrodes, the reset period may, for one embodiment, include a discretenumber of conductive electrodes for the largest angle, and moreelectrodes for a smaller angle. An eight-cell configuration would limitloss due to quantization to 5%, as explained in Reference 1. Dependingupon the desired steering efficiency, certain embodiments may have asfew as a three-cell configuration, although any number of cells may beprovided including six, eight, ten, fifteen, or twenty cells before eachreset period. As the modulation of the optical or photonic wave by theoptically active cells is accumulative, an optional reflective layer canbe added as the last layer of the scanner to provide either moredeflection angle, or smaller cell thickness, by having the optical orphotonic wave pass through the phase delay areas a second time.

An example embodiment includes the scanner made of at least twooptically active layers interposed between two substrates. Eachoptically active row contains an array of cells whose index ofrefraction can be changed in one or both polarizations, such as liquidcrystal, quantum dot, or EO crystals, such as SBN, PMN-PT, KTN, and/orBaTiO₃. An example embodiment includes each active cell sandwichedbetween electrodes that are either conductive, or resistive. In theexample embodiment, there is an insulator cell between every opticallyactive cell in each row, and the arrangement of optically active cellsand insulator cells is opposite in each row. In one embodiment the widthof any corresponding cells in the different rows is exactly the same, solight undergoes an OPD associated with one active layer for each pair ofactive layer/insulator sections. The corresponding cells are aligned soone layer provides OPD, which for a given wavelength corresponds to agiven phase shift, in one cell pair, and the second layer provides OPD,or phase shift, in the second cell pair.

In certain embodiments, the insulator cells, and substrates, are made ofa material which has the same or a similar index of refraction, and istransparent (or sufficiently transparent) to the incoming optical wave.In one embodiment, all layers of the scanner are planarized to a surfaceflatness of one fiftieth ( 1/15) or better of the wavelength of theincident EM wave. The indices of refraction of the substrate, the activematerial, and the insulator cells should be similar, or it will beadvantageous to apply an anti-reflecting coating on every discontinuitybetween materials to enhance the steering efficiency. A transmissiveoptical or photonic beam scanner can be made reflective if the lastelectrode is reflective, or a reflective layer is coated on one of thesubstrates. In certain embodiments, for example where accurate opticalquality of the steered EM beam is not required for a particularapplication, the insulator cells, substrates, and/or active cells mayhave optical characteristics that are not similar, or that varysignificantly.

In another embodiment of the present disclosure, the scanner can be madeof two or any even number of optically active rows. In the exampleembodiment, each two optically active rows are interposed between twosubstrates, and/or a number of optically active rows are bounded by twosubstrate layers at opposing ends of the beam steering device. Each tworows are separated from each other by a common continuous transparentground electrode. Each row comprises an array of optically active cellssandwiched between two electrodes that are either conductive orresistive, and an insulator cell is positioned between adjacent EOcells. In the example embodiments, the arrangement of EO cells andinsulators are reverse in each row, and the size of the active cells ineach row will be the same as the size of the corresponding insulatorcells in the next row.

In certain embodiments, the insulator cells and substrates are made of amaterial with the same index of refraction and are transparent to theincoming optical or photonic wave like IR glass or SrTiO₃. The EO cellsare made of any materials whose index of refraction can beelectronically changed in one or both polarizations, like liquidcrystal, quantum dot, or EO crystals like SBN, PMN-PT, KTN, BaTiO₃. Incertain embodiments, the layers of the scanner are planarized to aselected surface flatness to achieve the desired optical quality and/orsteering efficiency. Example and non-limiting surface flatness valuesinclude a surface flatness of one-tenth, one-twentieth, one-fortieth,and/or one-fiftieth or better of the target wavelength. The indices ofthe substrate, active and insulator cells are close otherwise ananti-reflecting coating may be required on every edge where materialdiscontinuity occurred. That agile transmissive optical or photonic wavescanner can be realized as reflective one if a reflective layer iscoated on one of the substrates and/or on a common ground electrode.

One approach to determine the value from which OPD is subtracted (e.g.,for a reset) is given in Gregor Thalhammer, Richard W. Bowman, Gordon D.Love, Miles J. Padgett, and Monika Ritsch-Marte, “Speeding up liquidcrystal SLMs using overdrive with phase change reduction,” 28 Jan.2013/Vol. 21, No. 2/OPTICS EXPRESS p 1779-1797. The Thalhammer paper isincorporated herein by reference in the entirety for all purposes. Fineangular beam steering may also result in subtracting the reset from avalue not exactly an increment of 2πn phase shift. The article byBurrell R. Hatcher, “Granularity of beam positions in digital phasedarrays,” Proceedings of the IEEE (Volume: 56, Issue: 11, November 1968,teaches very fine angular steering using a phased array, but initiatingthe subtraction of a multiple of one wavelength of OPD from a value thatis not an exact multiple of one wavelength of OPD, or 2πn of phase. TheHatcher paper, which may be referred to as “Reference 5” hereinafter, isincorporated herein by reference in the entirety for all purposes. Thefly-back effect is a result of the inability of the device to change itsvoltage profile instantaneously between two sets of electrodes, which isshown in FIG. 2. The fly-back region in FIG. 2 is the region for whichthe OPD or phase decreases as the distance increases.

Many modulo 2π steering embodiments, such as liquid crystals, or anelectro-optical crystal, create an index change in one polarization as aresult of applying an Electric, or E, field in the device as is shown inFIG. 11. Other materials, such as quantum dots, can change the index inboth polarizations when voltage is applied. An external electric fieldwill be applied on the medium by applying voltages on those electrodes.The external electric field manipulates the refractive index of themedium in one, or more, polarizations. The medium must be transparent(or sufficiently so) to the incoming light and can be liquid crystal, anelectro optical crystal, a quantum dot material or any other materialswhose refractive index can be manipulated by applying an externalelectric field. Monochromatic light can be deflected if a sawtooth phaseprofile is provided. The inability to precisely control those electricfields due to fringing effects results in similar inability to rapidlychange phase shifts, and an inability to create a sharp index change,and a sharp OPD change, therefore an inability to rapidly change OPD.The fly-back region reduces the fill factor of the optical grating wherefill factor is defined as the percentage of the beam steered in thedesired direction.

Fringing fields are the main reason for a fly-back region greater thanzero. For liquid crystals there can also be an inability of the liquidcrystal to change orientation quickly, but fringing fields are often amore limiting effect. FIG. 2 shows that during the fly-back portion ofthe phase profile the beam steers in the wrong direction. The followingequation gives the efficiency due to fly-back effects.

$\begin{matrix}{\eta = {\left( {1 - \frac{\Lambda_{F}}{\Lambda}} \right)^{2}.}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In equation 1, η is efficiency, Λ_(F) is the width of the fly-backregion, and Λ is the width between resets. Equation 1 is taken from P.F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S.Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp,and E. A. Watson, “Optical Phased Array Technology,” Proc. IEEE 84(2),268-298, 1996. The McManamon reference “Optical Phased ArrayTechnology”, which may be referred to as “Reference 4” hereinafter, isincorporated herein by reference in the entirety. This is the fringingfield limited steering efficiency.

The following equation provides fly-back distance vs steeringefficiency, for steering efficiency limited by fly-back.Λ_(F)=Λ(1−√{square root over (η)})  Equation 2.

FIG. 2 shows fringing fields make it impossible in a traditional thinsteering device to impose an electric field that results in oneelectrode, or less, wide resets while using small electrodes andsteering to large angles with commercially available materials havingnormal index change ratios. As a rule of thumb, the narrowest width of areset is about the thickness of the device layer between the electrodesand the ground plane, as discussed in X. Wang, B. Wang, P. F. McManamon,J. J. Pouch, F. A. Miranda, J. E. Anderson, P. J. Bos, “Spatialresolution limitation of liquid crystal spatial light modulator,” LiquidCrystal Conference, Great Lakes Photonics Symposium, Cleveland, OhioJun. 7-11, 2004. The Wang reference “Spatial resolution limitation . . .” is incorporated herein by reference in the entirety.

Fringing fields can have a significant limiting effect on presentlyknown modulo 2π beam steering devices. For transmissive beam steeringthe cell must be at least approximately as thick as required to obtainone wavelength, or generate 2π phase, of OPD. A birefringence of 0.3means the cell must be about 3.3 times one wavelength in thickness.Table 1 gives the fringing field effect on the steering efficiency for a0.35 index of refraction change using transmissive beam steering. Forelectro-optic active materials having an index of refraction changelower than 0.35, the steering efficiency values will be lower than thosedepicted in Table 1.

TABLE 1 Efficiency vs. Angle limited by fringing field effects forpreviously known modulo 2π beam steering devices Angle (deg) Angle (rad)Index change Efficiency 20 0.349 0.35  0.0% 15 0.262 0.35  6.3% 10 0.1750.35 25.0% 5 0.087 0.35 56.5% 2.5 0.044 0.35 76.4% 1.5 0.026 0.35 85.7%1 0.017 0.35 90.5% 0.625 0.011 0.35 93.8% 0.25 0.004 0.35 97.7% 0.150.003 0.35 98.3% 0.1 0.002 0.35 98.9%

Table 1 shows that efficiency drops off rapidly for previously knownmodulo 2π beam steering at significant steering angles. If highefficiency is desired, then the steering angles used for previouslyknown modulo 2π beam steering devices must be limited to very smallangles. The fringing field efficiency losses are incurred for eachsteering event—for example if a 1 degree steering in both azimuth andelevation is performed, then the realized efficiency will be(0.905){circumflex over ( )}2, or about 82% resulting efficiency. Anexample modulo 2π steering device consistent with the present disclosureutilizes a reflective beam steering, light goes into the device, bouncesoff a reflecting surface, and returns. As a result, the active devicelayer is half as thick and the fly-back region is half as wide, thusincreasing the steering efficiency.

In certain embodiments, an optical phased array (OPA) non-mechanicalbeam steering includes the ability to point to less than 1/100^(th) of adiffraction limited angular spot size very accurately. For manyapplications, including high-energy applications and/or operationsperformed in sensitive areas, the ability to steer to the desired anglesis very important. Modulo 2π beam steering using OPA technology canenable very precise steering, for example as explained in Reference 5.

Another factor is the steering efficiency due to quantization, which isdescribed in the following equation from Reference 3:

$\begin{matrix}{\eta = {\left\lbrack \frac{\sin\left( \frac{\pi}{q} \right)}{\left( \frac{\pi}{q} \right)} \right\rbrack^{2}.}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

In equation 3, η is the steering efficiency, and q is the number ofsteps for each 2π phase shift progression of the steering device.Accordingly, eight (8) steps result in 95% steering efficiency fromquantization, and ten (10) steps result in 96.8%. Any loss forquantization is additional loss compared to loss from fringing fields.Actual loss due to quantization for a few selected step values will beas shown in table 2:

TABLE 2 Quantization loss. No of steps Efficiency  2   41%  3   68%  5  88%  6   91%  8   95% 10 96.8% 12 97.7% 16 98.7% 20 99.2%

Another background issue is the effect of magnification. A beamdeflector having a small beam passing through it, when magnified, willdecrease the steering angle, as shown in the following equation:

$\begin{matrix}{\vartheta_{f} = {\frac{\vartheta_{i}}{M}.}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

In equation 4, ϑ_(f) is the final steering angle, M is themagnification, and ϑ_(i) is the initial steering angle. For example, a 5mm wide beam passing through a crystal and magnified to a 100 mm widebeam requires a magnification factor of 20. Therefore, a 10-degreesteering angle is reduced to a half of a degree for this example with amagnification of 20.

Referencing FIG. 3, a previously known bulk beam steering device isdepicted to illustrate certain differences relative to various systemsand methods in the present disclosure. In bulk beam steering, lightpasses through an EO crystal, and is steered. Under current practice,incident light with linear polarization in the proper direction isdeflected and the angle of steering is varied by the application of anelectric field. The angle of deflection for the conventional bulk beamdeflector is calculated as:

$\begin{matrix}{\theta_{f} = {\frac{L\;\Delta\; n}{W}.}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

In equation 5, θ_(f) is the deflection angle, Δn is the index changeoccurred by the applied voltage and L and W are length and width of therectangular beam deflector.

Previously known bulk beam steering devices suffer from a number ofdrawbacks. For example, when the optical beam is larger than a crystal,the beam is focused into the crystal and is expanded afterward. Thatrequires large magnification, which reduces the effective steering angleas discussed preceding. Additionally, previously known bulk beamsteering devices require significant voltages to be developed within thecrystal, which may be thousands of volts. These high voltages areundesirable and introduce a number of challenges in management of theoperating device, material selection and device design, and potentialsafety issues. The beam steered by a bulk beam steering device such asin FIG. 3 will likely be collimated when it traverses the crystal.

FIG. 4 depicts a previously known bulk beam steering device performing atwo-dimensional beam steering using two bulk crystals, and a halfwaveplate between. In addition to the necessity of a half wave plate torotate the polarization direction of the incident light by 90 degrees,some lenses may also be required between the two crystals to ensure thebeam enters the second crystal.

As seen in FIG. 4, one dimension will be steered first, possibly in onecrystal, and then the other dimension will be steered, possibly in asecond crystal. The linearly polarized light deflected in one-dimensiontravels through the second crystal to be steered in another dimensionafter its polarization direction is rotated by the half wave plate.Therefore, when the beam exits the first crystal it is deflected to acertain angle. That beam direction is maintained in the second crystal.A difficulty with this geometry is that the deflection angle must bekept small, or the beam will hit the side wall of the second crystal.The deflection of the beam inside of a crystal, resulting in thepossibility of hitting the wall, is often called beam walk off by thosepracticed in the art.

Referring to FIG. 11, an example modulo 2πn scanner comprises an activerow made of an EO layer 3 (e.g., an EO active layer that changes anoptical characteristic in response to an applied voltage) sandwichedbetween two sets of transparent discrete electrodes. The EO material maybe any type of material that changes an optical characteristic inresponse to an applied voltage, including at least an EO crystal, acrystal layer, multiple crystal layers, an EO crystal layer, multiple EOcrystal layers, a liquid crystal, a polymer, a quantum dot device, acrystal that responds to an applied electric field with a linear changein an index of refraction, and/or a crystal that responds to an appliedelectric field with a quadratic change in an index of refraction. Anoptical characteristic that changes in response to an applied voltageincludes a change in birefringence and/or refractive index in responseto an applied electric field. In certain embodiments the change may bedependent upon wavelength, polarization, and/or propagation direction ofthe steered EM beam. In certain embodiments, the change may be linear ornon-linear. Without limitation to any other aspect of the presentdisclosure, it will be understood that descriptions utilizing an EOactive layer, an active layer, an EO material, and/or a crystal mayadditionally or alternatively include any other EO active materialsdescribed throughout the present disclosure.

One of skill in the art, having the benefit of the disclosure herein,can readily select an appropriate EO material for a particular system.Certain considerations for material selection include, withoutlimitation: the cost of materials, the steering capability (e.g.,required electric field and/or optical change amount), the response timeof the material in changing an optical characteristic, the cost of thematerial, fabrication considerations for the material (e.g., includingavailable methods of fabrication, capability of the fabrication processfor the material to achieve a particular design state, and/or cost ofthe fabrication process), the physical strength of the material asconfigured in a beam steering device, and/or thermal capability of thematerial (e.g., ability to withstand heat generation and/or support heatrejection). Certain considerations of a system when contemplatingparticular materials include, without limitation: the amount of steeringdesired; capital costs versus operating cost trade-offs; the energythroughput of the application; the available configurations for EM beamdirection, polarization, and/or wavelength options; the desired accuracyand precision of beam steering direction, energy delivery, and/oroptical characteristics of the steered beam; the availability ofcomputing power in the device or accessible to the device to providecompensation, control, and/or analysis of electrical components and/oroptical components in the device; and/or the size of the beam steeringdevice (e.g., influencing the size of each layer, the number of layers,and/or the geometric configuration of the fabricated layer).

In the example of FIG. 11, the upper electrodes 2 are high-sideelectrodes making up a high-side electrode layer, and the lowerelectrodes 4 are low-side electrodes making up a low-side electrodelayer. In the example, the lower electrodes 4 may be at a ground statevoltage, or another low voltage or baseline voltage value. The upperelectrodes 2 may be at selected voltages thereby providing selectedvoltage differentials across the portions of the EO layer 3, therebycreating active cells of the EO layer 3. The EO layer 3 is interposedbetween two substrates 1 in the example of FIG. 11. The description ofupper electrodes 2 and lower electrodes 4 is an electrical descriptionand not a geometrical description, and the upper electrodes 2 may be ona vertically upper side or vertically lower side of the EO layer 3, oron a side, oblique, or any other arrangement. In certain embodiments,one or more of the lower electrodes 4 may instead be a continuous oruniform electrode, such as a uniform ground electrode (e.g. referenceFIG. 12 with ground electrode 670). In certain embodiments, the lowerelectrodes 4 (and/or uniform ground electrode 670) may be transparent,sufficiently transparent at selected EM wavelengths, reflective, and/orincludes or is coupled with a reflective layer. In certain embodiments,the substrate 1 is transparent, sufficiently transparent at selected EMwavelengths, and/or includes or is coupled with a reflective layer. Inthe example of FIG. 11, Light is propagating perpendicular to thesubstrate 1 through the EO crystal layer 3, and may progress through theupper electrodes 2 or the lower electrodes 4 first, and then through theother of the upper electrodes 2 or the lower electrodes 4 second.

Referring to FIG. 5, an embodiment of this disclosure comprises a set oftransparent discrete electrodes 30 and a ground electrode 40 located onopposite sides of an EO active layer 10. The ground electrode can beeither reflective or transparent to the incoming light. Discreteelectrodes 30 can be either conductive or resistive. The discreteelectrodes may replace the uniform ground electrode 40 in someembodiments. Light is propagating perpendicular to the EO crystal layer10, or at some angle with respect to the ground electrode 40, throughthe EO crystal layer 10, toward the discrete electrodes.

Note, the terms “crystal,” “EO crystal,” “crystal layer” and “EO crystallayer” are used interchangeably herein and refer to any media who'sindex of refraction, or birefringence, can be changed by the applicationof an electric field. The crystals of this disclosure may includecrystals with either a linear, or quadratic, change in index ofrefraction with respect to an applied field. The term crystals may alsoinclude liquid crystals, or any media whose index of refraction can bechanged by application of an electric field. If transparent electrodesare used on both side of the structure shown in FIG. 5, then to achievelarger steering angles one embodiment could use multiple stackedstructures.

In FIG. 5, Ground electrode 40 can be either transparent or reflective.In case of having transparent ground electrode 40, it may be a singleelectrode as shown, or may be a series of electrodes similar to discreteelectrodes 30 located on the other side of the EO crystal layer 10. Ifthe ground electrode 40 is a series of electrodes, said series ofelectrodes 40 do not have to all be set at zero voltage, even though theterm ground is used.

The use of insulators 20 between electrodes 30 reduces the fly-backdiscussed in the background section for modulo 2π beam steering devices.This will allow steering to larger angles at high efficiency, because itwill reduce the fringing field effects on the electric field. In certainembodiments, the insulators 20 may be a dielectric material, and/orinclude a dielectric material or layer as a part of the insulators 20.In previously known modulo 2π beam steering devices, there issignificant spreading of the electric field, referred to as fringingfields, which is a primary contributor to the fly-back effect. Theexample embodiment of FIG. 5, having the insulator 20 between electrodes30, reduces the spreading of the electric field between electrodes. Thetransparent discrete electrodes 30 can be conductive or resistive. Inboth cases the fly-back distance will be reduced significantly but thephase diagram will be different whether those are conductive orresistive. As described preceding, FIG. 6 shows an example phase diagramand the sharp reset provided when discrete electrodes 30 are conductive,and FIG. 8 shows the phase diagram and the sharp reset provided when thediscrete electrodes 30 are resistive discrete electrodes and/orelectrodes configured to provide an optimum set of voltages across theactive cells.

In one embodiment, the crystal layer 10 may have a resistivity that maybe much lower than the insulator 20, for example 100 times lower. Thisis estimated to reduce the fringing electric field spreading effect byfor example a factor of approximately 100 times in the insulator 20. Thewidth of the insulator 20 can influence the amount of fringing fieldreduction. The quality of the insulator may also influence the amount offringing field reduction, with a less conductive insulator providingmore reduction in fringing fields. The insulator 20 may extendcompletely through the crystal layer 10 whose index can be changed by anelectric field or the insulator 20 may only extend part way through thecrystal layer 10. For example, the insulator 20 may extend anywhere fromless than 10% to more than 80% through the crystal layer 10, or it canextend 100% of the way through the crystal. As a result, sharper resetsare realized when the OPD is reduced during a reset from approximately amultiple of one wave, or a multiple of one wavelength, to approximatelyzero. Consequently, an OPD profile with sharper resets results, andhigher steering efficiency is realized.

Comparing FIG. 2 with FIG. 6 shows that the electric field will increasein more discrete step increments than without the insulator 20separating the discrete electrodes 30, rather than being smoothed byfringing fields, and the resets will be much sharper. An exampleembodiment utilizes partial penetration of the crystal layer 10 by theinsulators 20 to retain and/or configure some smoothing of the fringingfields on the increasing phase ramp. An example embodiment utilizespartial penetration of the crystal layer 10 by the insulators 20 as apractical consideration in creating the insulators 20 within the crystallayer 10—for example to enable easier fabrication and/or an improvedmechanical structure of the beam steering device. In certainembodiments, insulators 20 provided at a reset position are enhanced(e.g., higher resistance and/or impedance, greater thickness, and/or agreater penetration of the crystal layer 10), providing for smoothingeffects on the increasing phase ramp portion with greater fringing fieldresistance at a reset position.

Referring to FIG. 7, another embodiment of this disclosure comprisestilted electrodes 50 instead of electrodes on the surface of the EOcrystal layer 10. This embodiment will reduce, or eliminate, thequantization effect of the steps in building up the electric field. Thisembodiment further comprises an EO crystal layer 10, a ground electrode40 and insulators 20. Ground electrode 40 includes, but is not limitedto transparent ground electrodes. The transparent ground electrode 40may be a single electrode as shown, or may be a series of electrodes.Once again, insulators 20 may extend fully or partially through EOcrystal layer 10. The tilted electrodes 50 may progress in anyconfigured manner through the EO crystal layer 10, as describedthroughout the present disclosure.

For the tilted electrode embodiment shown in FIG. 7, the electric fieldon adjacent discrete tilted electrodes 50 is made continuous, or nearcontinuous, by reducing the distance between the discrete electrodes 50and the ground electrodes 40 using a fixed tilt angle. While the fixedelectrode tilt angle may not be ideal for all steering angles, it willreduce the quantization effect over a wide range of steering angles. Asshown in FIG. 8, an increase in applied voltage is compensated by thedistance change to provide a continuous, or near continuous, electricfield at any adjacent discrete tilted electrode 50 before reset.

Another embodiment (not shown) using the insulators would be toimplement modulo 2π beam steering using liquid crystals to cause achange in index of refraction. Any material that can have an index ofrefraction change in one polarization could be used with the insulatorsbetween conductive or resistive electrodes. The insulators can also belocated between the electrodes with a depth between zero to the liquidcrystal thickness, depending on the desired steering efficiency.

As seen in FIG. 9 and FIG. 10, a mirror layer 60 can be added after theground electrode layer 40 and/or as a layer on the substrate. If a stackof structures is used the mirror layer would be after the full stack ofdevice layers. This will increase the deflection angle allowed at acertain steering efficiency by reducing the required cell thickness, andthe fly-back region distance.

An example embodiment consistent with the depiction of FIG. 12 isdescribed following. An embodiment comprises two optically active rows610, 620 interposed between two substrates 600, 605. Each row containsan array of active cells 630 which active cells are separated from eachother by insulator cells 640. The active cells 630 are made of anoptically active material, and are sandwiched between a continuousground electrode 650 and discrete electrodes 660. The discreteelectrodes may be either conductive or resistive. The arrangement ofactive cells 630 and insulator cells 640 is opposite in each row. Thesize of an active cell 630 in a row 610, 620 is the same as the size ofthe corresponding insulator cell 640 in the next row. The last groundelectrode 670 can be either reflective or transparent to the incominglight to be deflected by the scanner.

An example embodiment consistent with the depiction of FIG. 13 isdescribed following. An embodiment depicted in FIG. 13 is similar to theembodiment shown in FIG. 12 but comprises four active rows 680, 685, 690and 695. The four active rows 680, 685, 690 and 695 are interposedbetween two substrates 710 and 720. The embodiment can comprise any evennumber of active rows, and/or may include odd numbers of active rows,for example with one or more repeating rows. Each active row comprises aground electrode 730, with the last ground electrode 700 being eitherreflective, or transparent, to the incoming light to be deflected by thescanner. Similar to the embodiment shown in FIG. 12, each of the activerows contain an array of active cells 740. The active cells areseparated from each other by insulator cells 750. The active cells 740are made of an optically active material and are sandwiched between acontinuous ground electrode 700, 730 and discrete electrodes 760, whichmay be either conductive or restrictive. The ground electrode could bein discrete elements in another embodiment. The arrangement of activecells 740 and insulator cells 750 is opposite in each row. The size ofan active cell 740 in a row 680, 685, 690 and 695 is the same as thesize of the corresponding insulator cell 750 in the next row. While FIG.13 shows two pairs of rows, for a total of 4 rows, the number of rowsmay be any number, including any multiple of two rows or otherarrangements.

An example embodiment consistent with the depiction of FIG. 14 isdescribed following. An embodiment of a scanner comprises two opticallyactive rows 770, 775 separated by a common transparent continuous groundelectrode 780. Each of the active rows 770, 775 are interposed betweentwo substrates 805, 807. Each row contains an array of active cells 790.The active cells 790 are separated from each other by insulator cells800. The active cells are made of an optically active material and aresandwiched between a continuous ground electrode 780 and discreteelectrodes 810, which may be either conductive or resistive. Thearrangement of active cells 790 and insulator cells 800 is opposite ineach row. The size of an active cell 790 in a row 770, 775 is the sameas the size of the corresponding insulator cell 800 in the neighboringrow. A reflective layer 820 can be located on a surface of the substrate805 to make the scanner reflective.

An example embodiment consistent with the depiction of FIG. 15 isdescribed following. An embodiment of a scanner depicted in FIG. 15 issimilar to the embodiment shown in the FIG. 14 but comprises four activerows 830, 840, 850, and 860 instead of just two active rows. Theembodiment can comprise any even number of active rows, and/or mayinclude odd numbers of active rows, for example with one or morerepeating rows. Each two rows are separated by a transparent continuousground electrode 780 and each pair of rows is interposed by twosubstrates. More specifically, a first pair of rows is interposedbetween substrates 870 and 872 and a second pair of rows is interposedbetween substrates 872 and 875, as shown in FIG. 15. Each row containsan array of active cells 790. The active cells 790 are separated fromeach other by insulator cells 800. The active cells are made of anoptically active material and are sandwiched between a continuous groundelectrode 780 and discrete electrodes 810, which may be eitherconductive or resistive. The arrangement of active cells 790 andinsulator cells 800 is opposite in each row. The size of an active cell790 in a row is the same as the size of the corresponding insulator cell800 in the neighboring row. A reflective layer 890 may be located on asurface of the substrate 870 to make the scanner reflective. While FIG.15 shows two pairs of rows, for a total of 4 rows, the number of rowsmay be any number, including any multiple of two rows or otherarrangements.

In FIGS. 12-15, the light is initially propagating perpendicular to thesubstrate through the active cells, toward the discrete electrodes, orat some initial input angle to perpendicular. In FIGS. 12-15, thediscrete electrodes can be either conductive or resistive. In the caseof conductive discrete electrodes, only one voltage at the same time isapplied on each discrete electrode and a reset will usually containeight or more discrete electrodes in order to achieve 95% steeringefficiency, or better, based on quantization loss. In case of resistiveelectrodes, two, or more, different voltages at the same time may beapplied on each discrete electrode, and a reset may contain only one ormore discrete electrodes. Moreover, in the embodiments depicted in FIGS.12-15, the active cells are made of any transparent material whoserefractive index can be changed by applying voltages on the discreteelectrodes. Such transparent materials include but are not limited to EOcrystals like PMN-PT, KTN, SBN, PBN, PZT, BaTiO₃, liquid crystals,and/or quantum dot materials.

Referencing FIG. 16, an example embodiment of a beam steering device isdepicted. The example of FIG. 16 includes two active layers, with an EOactive material 1606 providing a number of active cells, each activecell positioned between one of a number of discrete high-side electrodes1610 and a low-side electrode 1612 (depicted as a common groundelectrode in the example of FIG. 16). The example beam steering deviceincludes insulators 1608 positioned between each of the high-sideelectrodes 1610, and a substrate 1602, 1604 provided on each side of theactive layer. The example of FIG. 16 may additionally include moreactive layers, and the substrate 1602, 1604 may be positioned betweeneach active layer and/or book-end the active layers. The example of FIG.16 is similar to a Chess Pattern beam steering device, with offsetactive cells in adjacent active layers, such that an incident EM beampasses through one or the other of the active layers. FIG. 16 includes abridging portion 1614 of the EO active material 1606 across theinsulation region (1608), which may provide for ramp smoothing of theprogressive phase delay, and/or may provide for easier fabricationand/or improved mechanical properties of the beam steering device.

Referencing FIG. 17, an example embodiment of a beam steering device isdepicted. The example of FIG. 17 includes two active layers, with an EOactive material 1706 providing a number of active cells, each activecell positioned between one of a number of discrete high-side electrodes1710 and a low-side electrode 1712 (a shared common ground electrode inthe example of FIG. 17). The example beam steering device includesinsulators 1708 positioned between each of the high-side electrodes1710, and a substrate 1702, 1704 provided on each side of the activelayer. The example of FIG. 17 further includes a reflective layer 1716.The example of FIG. 17 may additionally include more active layers, andthe substrate 1702, 1704 may be positioned between each active layerand/or book-end the active layers. The example of FIG. 17 is similar toa Chess Pattern beam steering device, with offset active cells inadjacent active layers, such that an incident EM beam passes through oneor the other of the active layers. FIG. 17 includes a bridging portion1714 of the EO active material 1706 across the insulation region (1708),which may provide for ramp smoothing of the progressive phase delay,and/or may provide for easier fabrication and/or improved mechanicalproperties of the beam steering device.

Referencing FIG. 18, an example embodiment of a beam steering device isdepicted. The example of FIG. 18 includes one active layer providingapproximately 100% fill efficiency within a single active layer. Theexample of FIG. 18 includes an EO active material 1806 providing anumber of active cells, each active cell positioned between one of anumber of discrete high-side electrodes 1810, 1811 and a low-sideelectrode 1812 (a common ground electrode in the example of FIG. 18).The example beam steering device includes a substrate 1804—in theexample of FIG. 18, the substrate 1804 provides an insulating functionfor the active layer, and portions of the substrate 1804 positionedbetween high-side electrodes 1810 may be considered insulators asdescribed throughout the present disclosure. The example of FIG. 18further includes a substrate 1802 opposing the substrate 1804, and areflective layer 1816 coupled to the substrate 1804. The example of FIG.18 includes a number of active cells formed from a single active EOsubstrate 1806, having varying thicknesses 1818, 1820. An example beamsteering device includes the first thickness 1818 being a wavelength ofa target EM beam, one-half of a wavelength of the target EM beam (e.g.,in embodiments having a reflective layer 1816), and/or being a discretenumber of wavelengths and/or half wavelengths of the target EM beam. Theexample beam steering device further includes the second thickness 1820being at least one-half wavelength greater than thickness 1818, or onefull wavelength greater than thickness 1818. In certain embodiments,thickness 1818 is one wavelength (λ), and thickness 1820 is twowavelengths (2λ). In certain embodiments, the voltage applied acrosseach active cell is adjusted to provide the desired phase delay profile,and/or the width of the active cells having varying thicknesses 1818,1820 is varied to provide the desired phase delay profile. In certainembodiments, a beam scanner having two (or more) active thicknesseswithin a single active layer, such as depicted in FIG. 18, is describedas a Castle Scanner and/or Castle Pattern. In certain embodiments, whereresistive high-side electrodes 1810, 1811 are utilized with a CastlePattern, such a beam scanner is described as a Castle Scanner Pro or aCastle Pattern Pro. The terminology of Castle Scanner or Castle ScannerPro embodiments is used for convenience and clarity of the descriptionherein. The example of FIG. 18 provides for a number of advantages incertain embodiments of the present disclosure, including asimplification of fabrication of the beam steering device, enhancedmechanical integrity of the beam steering device, and/or a smallervertical footprint of the scanner (e.g., along the axis of propagationof the incident EM beam) for a given steering capability.

The present disclosure throughout provides for specific examples forclarity of description and to show the inter-operability of variousfeatures of the disclosure. Embodiments described may be combined inwhole or part, and/or certain described features may be omitted,according to the capabilities desired for a particular system. Forexample, resistive electrodes may be utilized for some or all of thehigh-side electrodes in any of the described embodiments. Active cellthicknesses may be progressed and may vary in any active layer, orbetween active layers, in any of the described embodiments. Insulatorsmay be provided as an explicit device (e.g., as in FIG. 12 or 16) and/ormay be included as an air gap or a substrate portion (e.g., as in FIG.18). Low-side electrodes may be at any voltage value, including abaseline or zero reference voltage, any voltage lower than the high-sideelectrodes (during steering operations), and/or at a negative referencevoltage. Electrodes may be provided as tilted or contoured electrodes inone or more portions of the beam steering device, or throughout the beamsteering device. All or portions of the beam steering device may beprovided as a Chess arrangement, a Castle arrangement, or any otherarrangement described throughout the present disclosure.

The present disclosure describes active layers steering an incident EMbeam. It is understood that the steering of the EM beam may be in asingle direction (e.g., X or Y, azimuth or elevation, etc.) and/or for asingle polarity of the EM beam, and that additional layers may beprovided to include additional steering in other directions, in anotherpolarity, and/or to provide incremental steering for the first directionand/or polarity.

Certain further example systems are described following. While certainexample embodiments and figures of the present disclosure may be recitedfor clarity of the description, it will be understood that any of thesystems, devices, techniques, or processes throughout the presentdisclosure may be incorporated into and/or performed by the describedexample systems. An example system includes a high-side electrode layerhaving a number of discrete electrodes, a low-side electrode layer, andan electro-optic (EO) layer including an EO active material at leastpartially positioned between the high-side electrode layer and thelow-side electrode layer. The system thereby forms a number of activecells of the EO layer. The high-side electrode layer may be selectivelyenergized (e.g., with a supplied voltage), including at selected voltagelevels and/or with a voltage progression across the high-side electrodelayer (or a stage of the high-side electrode layer), thereby providing avoltage differential progression across the active cells and a selectedphase delay progression for an incident EM beam. Each of the number ofactive cells of the EO layer includes a portion of the EO layerpositioned between 1) a first one of the number of discrete electrodesof the high-side electrode layer, and 2) the low-side electrode layer.In certain embodiments, an active cell may be discrete from other activecells (e.g., reference FIG. 5, 7, 9, or 10), and/or an active cell mayform a portion of a continuous EO active material where the active cellsare the portions of the material between the high-side discreteelectrodes and the low-side electrode layer (e.g., reference FIG. 16,17, or 18). In certain embodiments, for example where a number ofsteering layers of a beam steering device are included, an active cellmay be considered an active cell for certain operating conditions orsystems (e.g., where an active cell is only utilized for certainwavelengths of light and/or for certain steering angles), and not anactive cell for other wavelengths of light. Accordingly, a system can beconstructed that supports multiple wavelengths of incident EM beams,that supports flexible steering capability, and/or that can beconfigured for a number of common wavelengths, where a single beamsteering device can then be configured after manufacture or even atrun-time to support the steering requirements for the application. Theexample system includes an insulator operationally coupled to the activecells of the EO layer, and at least partially positioned between a firstone of the active cells and a second one of the active cells. Forexample, insulators may be partially positioned between each activecell, positioned to completely separate each active cell, and/or have arange of insulating coverage in a given EO layer (e.g., to supportincreased insulation capability at a reset and/or to smooth the phasedelay profile using the flyback effect in a configured manner). Incertain embodiments, one or more active cells may not have insulators onone or more sides—for example a terminating active cell may not have aninsulator on a side that does have an adjacent active cell, and/or theutilization of the flyback effect on one or more active cells may bedesirable in certain instances as described in the present disclosure.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes the EO layer having at least six (6) activecells, at least eight (8) active cells, and/or between three (3) andtwenty (20) active cells. As described in the present disclosure, thenumber of active cells utilized in a phase delay progression stageresults in a change to the quantization efficiency, allowing for aconfigurable quantization efficiency value to support the goals of thesystem for a particular application. It can be seen that trade-offsbetween manufacturing constraints or costs, steering efficiency goals,and other parameters described herein and that are ordinarily availableto one of skill in the art contemplating a particular system can beutilized to select the number of active cells in a phase delayprogression stage. An example system includes the high-side discreteelectrodes including conductive electrodes, resistive electrodes, or acombination of conductive or resistive electrodes. In certainembodiments, a given electrode can be configurable to be conductive orresistive, for example using a solid state device responsive to commandsfrom a controller.

In certain embodiments, a system includes a selected number of theactive cells of the EO layer structured to apply a progressive phaseshift to an incident electro-magnetic (EM) beam, and/or where a next oneof the active cells of the EO layer after the selected number of activecells is configured to reset the progressive phase shift of the incidentEM beam by reducing the progressive phase shift by 2π, and/or by 2πn. Inthe example, the n includes a small positive integer value, for examplebetween 1 and 10 inclusive. The selection of the n value results incertain configuration changes for the beam steering device, including athickness of the EO active layer or portions of the EO active layer,and/or a voltage difference experienced within the beam steering device.In certain embodiments, a low n value provides for a very thin EO activelayer with very low voltage differences in the device. In certainembodiments, even selecting a high n value provides for a thinner EOactive layer and lower voltage differences in the beam steering devicerelative to previously known systems. For example, depending upon thewavelength of the incident EM beam to be steered and the opticalcharacteristics of the EO active material, an n value exceeding 10 oreven 20 can nevertheless keep device thicknesses below 20 μm (e.g., 700nm infrared*20=14 μm), and voltages in a reasonable range below 100V. Itwill be seen that the achievable thickness for the EO active layer, atleast in portions thereof, will be on the order of n*λ, or ½ of n*λ (fora reflective system), and voltages will be determined by the maximumsteering voltage prior to the reset. Example phase shift values for eachprogressive phase shift may be about 2π, or 2πn. For example, a phasedelay progression stage may provide for a phase delay progressionvarying from 0 to 2π over the course of the stage. However, the phasedelay progression stage may start at a value higher or lower than a 0phase shift, and end with a value higher or lower than 2πn (e.g., endingbefore or after a 360° phase shift in the cycle). Example andnon-limiting phase shift values for a phase delay progression stageinclude: a value between 1.5πn and 2.5πn, a value between 1.8πn and2.2πn, a value between 1.9πn and 2.05πn, a value of about 2πn, and avalue of 2πn. A value of about 2πn, and other phase delay approximationsas described herein, include at least variations from 2πn (or anotherbaseline value) that are close enough to support the desired steeringefficiency for a given application (e.g., including as part of an errorstack-up of multiple effects), a value that accommodates variation inmanufacturing (e.g., EO layer thickness, surface profile, materialvariation, electrode variance, etc.) for the beam steering device suchthat the phase delay approximation is not the limiting error in thesystem, and/or a value that is within one significant digit of thenominal value (e.g., 1.9πn to 2.1πn, where 2πn is the baseline value).

An example system includes where each of the number of insulatorsincludes at least one of a size or a resistivity selected in response toa voltage difference value of the corresponding active cells of the EOlayer, and/or where each one of the number of insulators positionedbetween a last one of the selected number of active cells and the nextone of the active cells is a reset insulator, and where the resetinsulator includes at least one of an increased insulation area or anincreased resistivity value. For example, a non-linear EO active layer(e.g., non-linear optical response to an electric field) may result inincreased voltage differences between active cells, which may becompensated with increased insulator capability at those positions. Inanother example, voltage differences at a reset position may be higherthan between other active cell pairs in the system, which may becompensated with increased insulator capability at those positions. Incertain embodiments, insulators may be capable of sufficiently isolatingany voltage differences in the system—for example to provide forconvenient manufacturing and/or to allow for configurability at designtime or run-time.

An example system includes where the EO layer has a thickness of atleast one wavelength corresponding to a target electro-magnetic (EM)frequency, and/or a thickness of one-half wavelength corresponding tothe target EM frequency (e.g., for a reflective system). In certainembodiments, the EO layer includes a progressive thickness value, wherea thickest portion of the progressive thickness value includes athickness of at least one wavelength corresponding to a targetelectro-magnetic (EM) frequency. In certain embodiments, a configurationwith tilted electrodes (e.g., reference FIG. 7) provides for an EO layerhaving a progressive thickness value, as the distance of the high-sideelectrode to the low-side electrode is varied across the active EO cell.An example system includes the EO layer including at least one materialsuch as: an EO crystal, a crystal layer, multiple crystal layers, an EOcrystal layer, multiple EO crystal layers, a liquid crystal, a polymer,a quantum dot device, a crystal that responds to an applied electricfield with a linear change in an index of refraction, and/or a crystalthat responds to an applied electric field with a quadratic change in anindex of refraction.

An example system includes where the high-side electrode layer, thelow-side electrode layer, and the EO layer together make up a firstphase delay progression stage, and where the system further includes asecond phase delay progression stage. The second phase delay progressionstage includes: a second high-side electrode layer including a number ofdiscrete electrodes; a second low-side electrode layer; a second EOlayer including an EO active material at least partially interposedbetween the second high-side electrode layer and the second low-sideelectrode layer, thereby forming a number of active cells of the secondEO layer. Each of the number of active cells of the second EO layerincludes a portion of the second EO layer positioned between 1) a firstone of the number of discrete electrodes of the second high-sideelectrode layer; and 2) the second low-side electrode layer. The examplesystem further includes a second insulator operationally coupled to theactive cells of the second EO layer, and at least partially positionedbetween a first one of the active cells and a second one of the activecells. In certain further aspects, an example system includes where thefirst phase delay progression stage and the second phase delayprogression stage are configured to additively steer an incidentelectro-magnetic (EM) beam (e.g., where the incident EM beam firstpasses through the first phase delay progression stage, and then passesthrough the second phase delay progression stage). In certainembodiments, the first phase delay progression stage steers an incidentelectro-magnetic (EM) beam along a first axis, and where the secondphase delay progression stage is configured to steer the incident EMbeam along a second axis, where the first axis is distinct from thesecond axis. In certain embodiments, the first axis may be perpendicularto the second axis (e.g., first steering in a horizontal axis, and thenin a vertical axis). It will be understood that the first and secondsteering axes may not be perpendicular, but may be selectively arrangedfor any steering configuration desired, and further it will beunderstood that the orientations of the first phase delay progressionstage and the second phase delay progression stages may be changed, suchthat the axis of the stage and the steering axis of the incident EM beamis not the same for each of the steering layers. In certain embodiments,the first axis corresponds to a first polarization of the incident EMbeam, and the second axis corresponds to a second polarization of theincident EM beam. In certain embodiments, the system includes a halfwave plate layer interposed between the first phase delay progressionstage and the second phase delay progression stage, where the half waveplate layer is structured to selectively rotate a polarization of theincident EM beam.

In certain embodiments, the low-side electrode layer includes acontinuous electrode across all or a portion of the EO active layer,and/or that may be shared by adjacent EO active layers (e.g., asdepicted in FIGS. 14 and 15). In certain embodiments, the low-sideelectrode layer may be at a ground voltage, a zero relative voltage, oranother voltage lower than the high-side electrode layer. In certainembodiments, the low-side electrode layer voltage may be a negativerelative voltage, and/or may be an adjustable voltage—for example wherethe low-side electrode layer voltage is pulled down during steeringoperations to a lower voltage value.

Certain embodiments include multiple EO layers (e.g., two or more EOlayers), where the multiple EO layers cooperate to steer an incident EMbeam in more than one axis (e.g., steering a first axis in a firstlayer, and a second axis in a second layer), to steer the incident EMbeam in more than one polarity (e.g., steering a first polarity in afirst layer, and a second polarity in a second layer), and/or to steerincident EM beams of more than one selected wavelength. In certainembodiments, steering incident EM beams of more than one selectedwavelength may include configuring the active layers (e.g., usinghigh-side electrodes responsive to a controller) to steer utilizingselected layer(s) from the multiple EO layers that are configured for acurrent incident EM beam wavelength, while leaving other layer(s) thatare configured for other incident EM beam wavelengths inactive duringthe steering of the current incident EM beam wavelength. In certainembodiments, the system to steer incident EM beams with more than onewavelength includes operations to switch between steered wavelengths,including switching which incident EM beam wavelength is being directedthrough the beam steering device, and which layers of the multiple EOlayers are currently active. In certain embodiments, switchingfrequencies may be high enough such that the target of the steered EMbeam cannot distinguish that different EM beam wavelengths are beingswitched (e.g., where the target exhibits a capacitive aspect inabsorbing steered EM energy). In certain embodiments, the switching isperformed to utilize multiple wavelengths of steered EM beams, and theeffect on the target, or noticeable by the target, is not aconsideration.

Referencing FIG. 19, an example controller 1902 structured to performcertain operations for steering multiple EM wavelengths is schematicallydepicted. The controller 1902 is depicted as a single device for clarityof description, although aspects of the controller 1902 may bedistributed across multiple devices, implemented in hardware and/or asinstructions stored on a computer readable medium, as sensors oractuators present in the system, and/or through network communicationsand/or remote processing capabilities.

An example controller 1902 includes a number of circuits structured tofunctionally execute certain operations of the controller 1902. Certainoperations are described in specific reference to FIG. 19, but anyoperations, procedures, or techniques throughout the present disclosuremay be implemented by, or performed by, a controller such as controller1902. The example controller 1902 includes an incident wavelengthcircuit 1904 that determines a wavelength value 1906 of an incident EMbeam, a steering configuration circuit 1908 that determines a first EOlayer command value 1910 and a second EO layer command value 1912 inresponse to the incident EM beam. A given system may include any numberof EO layers, and/or an EO layer may be a logical arrangement of activecells within one or more physical layers, for example with an area ofactive cells distributed across multiple physical layers making up an EOlayer. An EO layer command may include multiple commands to be providedto multiple electrodes, including voltage commands to high-sideelectrodes, and/or pull-down commands to low-side electrodes (e.g.,where one or more low-side electrodes are pulled to a lower voltageduring steering operations), such that a selected phase delayprogression is provided across the EO layer when the EO layer commandsare executed. In certain embodiments, EO layer commands further includea timing value that coordinates the EO layers—for example when thecontroller 1902 is steering multiple EM wavelengths in a sequencedand/or pulse-width modulated (PWM) operation. The example controller1902 further includes a steering implementation circuit 1914 thatprovides at least one of the first EO layer command value 1910 or thesecond EO layer command value 1912 to a steering control module 1916.

Operations of the controller 1902 may be performed during run-time ordesign time, or a combination of these. For example, where thewavelength of the incident EM beam to be steered is predetermined,operations of the incident wavelength circuit 1904 may be performed atdesign time, for example in the material selection and configuration ofactive cells, the geometry of active cells, the thickness of the EOlayer, the utilization (or not) of a reflective layer, the selectedparameters for insulators, and the design voltages of the electrodes(high-side and/or low-side). In the example, the EO layer commands 1910,1912 may be predetermined for the selected wavelength, and theoperations of the steering configuration circuit 1908 include providinga lookup of the EO layer commands 1910, 1912 (e.g., considering thewavelength value 1906, the configurations of one or more EO layers inthe system, and/or the amount and direction of steering that iscommanded). In the example, the steering implementation circuit 1914provides the EO layer commands 1910, 1912 to the steering control module1916 when the incident EM beam is active, during selected operatingperiods, and/or continuously. In the example, the steering controlmodule 1916 controls the electrode voltages to implement the EO layercommands 1910, 1912 in response to the commands provided by the steeringimplementation circuit 1914.

In another example, such as when the wavelength of the incident EM beamis configurable, selectable, and/or varies after initial construction ofthe beam steering device (e.g., to support multiple steeringconfigurations with a single hardware device, and/or to steer multipleEM beam wavelengths with a single hardware device), one or moreoperations of the incident wavelength circuit 1904 may be performed atrun-time. In the example, the incident wavelength circuit 1904determines the wavelength value 1906 at run-time, for example using anysensing technique known in the art, and/or by determining that anothersystem parameter is indicating that a particular wavelength value 1906is being utilized (e.g., a network parameter, a parameter provided byanother controller, an active state of a particular EM source, or thelike). In the example, the steering configuration circuit 1908determines the EO layer commands 1910, 1912 (e.g., considering thewavelength value 1906, the configurations of one or more EO layers inthe system, and/or the amount and direction of steering that iscommanded). In the example, the steering control module 1916 controlsthe electrode voltages to implement the EO layer commands 1910, 1912 inresponse to the commands provided by the steering implementation circuit1914.

Certain examples of operations of the controller 1902 are provided forclarity of the present description. It will be understood thatoperations of the controller 1902 may be provided in any combination ofdesign-time and/or run-time operations, and further that operations ofthe controller 1902 may be adjusted in response to the operatingconditions of the system, a change in the application of the beamsteering device including the controller 1902 (e.g., a change in thesteered wavelength, a change in the desired steering capability, and/ora change in the timing of multiple-layer steering operations), and/or inresponse to a change in a hardware configuration of the beam steeringdevice (e.g., a change in the EO layer, voltages of the system, and/or awavelength of an EM source).

An example steering control module 1916 provides selected voltages to atleast one of the first high-side electrode layer or the second high-sideelectrode layer in response to the at least one of the first EO layercommand value 1910 or the second EO layer command value 1912. An examplesteering control module 1916 further includes a solid state circuit thatapplies selected voltages to each electrode of the first high-sideelectrode layer and the second high-side electrode layer. An examplesolid state circuit further selectively couples a power source to eachelectrode of the first high-side electrode layer and the secondhigh-side electrode layer, and/or selectively couples the power sourceusing a pulse-width modulation (PWM) operation. In certain embodiments,a steering control module 1916 includes hardware elements configured toexecute operations to implement the EO layer command values 1910, 1912,for example solid state switches that are responsive to commands fromthe steering implementation circuit 1914. In certain embodiments, thesteering control module 1916 may be a smart controller, structured toprovide commands to implement the EO layer command values 1910, 1912 asprovided by the steering implementation circuit 1914. In certainembodiments, aspects of the steering control module 1916 may beimplemented on the controller 1902. Accordingly, it will be seen thatthe EO layer command values 1910, 1912 may vary, from low-level hardwarecommands (e.g., ON/OFF, or a voltage value sourced from or switched fromthe controller 1902) to high-level steering commands (e.g., steer 5degrees in the X axis with EO layer 2, and 7 degrees in the Y axis withEO layer 3), combinations of these, and/or intermediate parametersbetween these (e.g., voltage values indicating an amount of steeringand/or a layer to be controlled, simple state values which the steeringcontrol module 1916 is configured to be responsive to, or the like). Incertain embodiments, the steering control module 1916 may receive the EOlayer command values 1910, 1912 as physical values (e.g., voltages,frequencies, pressures, or another physical value), as networkcommunicated parameters from the controller 1902, and/or as parametersretrieved from the controller 1902 memory by the steering control module1916 (e.g., in a selected memory location that is populated by thesteering implementation circuit 1914). The example steering controlmodule 1916 hardware and operational examples are non-limiting, andprovided for clarity of the present description.

An example system includes an EO substrate layer including an EO activematerial and further including a number of thin elements alternatingwith a number of thick elements, a high-side electrode layer including anumber of discrete electrodes, each of the number of discrete electrodesassociated with one of the number of thick elements and positioned on afirst side of the EO substrate layer, and a low-side electrode layerpositioned on a second side of the EO substrate layer. The examplesystem further includes an insulator layer operationally coupled to theEO substrate layer, and at least partially positioned between each ofthe number of thick elements. In certain embodiments, the thin elementsmay additionally be active cells (e.g., reference FIG. 18), or the thinelements may not be active cells (e.g., reference FIG. 16). Where thethin elements are active cells, the thin elements may have a thicknessof at least ½ λ (e.g., with a reflective layer) or a thickness of atleast λ (e.g., with no reflective layer). In certain embodiments, thethick elements have a thickness of at least ½ λ more than the thinelements (e.g., with a reflective layer) or a thickness of at least λmore than the thin elements. It will be seen that the thickness betweenthe thin elements and the thick elements may be varied—for example whenthe thick elements are a part of a first active layer (e.g., cooperatingwith active cells in another physical layer of the beam steering deviceto provide beam steering of the incident EM beam) and the then elementsare a part of a second active layer (e.g., cooperating with active cellsin another physical layer of the beam steering device to provide beamsteering of the incident EM beam), such that no particular relationshipbetween the thin elements and the thick elements is required. In certainembodiments, such as when the thin elements and the thick elementscooperate to form an active layer of the beam steering device, thethickness of the thick elements and the thin elements may vary by amultiple of λ or ½ λ. An example system includes both the thin elementsand the thick elements having active cells, with the thin elementshaving a thickness of λ and the thick elements having a thickness of 2λ.In certain embodiments, a thick element of a first physical layer may bethinner than a thin element of a second physical layer.

An example system includes a number of the EO substrate layers, whereeach of the number of thin elements includes a thickness of xwavelengths corresponding to a target electro-magnetic (EM) frequency,where each of the number of thick elements includes a thickness of ywavelengths corresponding to the target EM frequency, where each of xand y comprise integer values, and where the y value for each of thenumber of thick elements is at least one greater than the x value for anadjacent one of the number of thin elements. In certain embodiments, thex value is one (1), and/or the y value is two (2). In certainembodiments, a first one of the number of thick elements includes a yvalue that is smaller than an x value for a first one of the number ofthin elements, for example where the first one of the number of thickelements is not adjacent to the first one of the number of thinelements. In certain embodiments, the first one of the number of thickelements is in a different one of the number of EO substrate layers asthe first one of the number of thin elements. In certain embodiments,for example where multiple physical layers are provided to steerdifferent target EM frequencies, the λ value for a first layer (e.g.,used to determine the thickness of thick and thin elements for a firstactive layer) is different than a λ value for a second layer.

An example system includes an EO substrate layer including an EO activematerial, and further including a number of active elements. The examplesystem includes adjacent ones of the number of active elements having athickness value varying by at least one wavelength corresponding to atarget electro-magnetic (EM) frequency. The example system furtherincludes a high-side electrode layer including a number of discreteelectrodes, each of the number of discrete electrodes associated withone of the number of active elements and positioned on a first side ofthe EO substrate layer; a low-side electrode layer positioned on asecond side of the EO substrate layer; and an insulator layeroperationally coupled to the EO substrate layer, and at least partiallypositioned between geometric gaps of the number of active elements.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes where the number of discrete electrodes areresistive electrodes; a number of the EO substrate layers, and where twoadjacent ones of the number of the EO substrate layers share a low-sideelectrode layer; where a terminating one of the number of EO substratelayers is associated with a reflective low-side electrode layer; and/orwhere the number of EO substrate layers are arranged such that aperpendicular line through the number of the EO substrate layers passesthrough a configured thickness of the active elements of the number ofthe EO substrate layers, the configured thickness including a thicknessselected to apply a progressive phase shift to an incident EM beam.

In certain embodiments, EO active layers having thick and thin elementsare referenced as a castle configuration herein. In certain embodiments,a castle configuration includes both the thick and thin elements makingup active cells of the beam steering device (e.g., having an associateddiscrete high-side electrode). In certain embodiments, a castleconfiguration includes adjacent physical layers of the beam steeringdevice having alternating thick and thin elements, such as that depictedin FIG. 16. In certain embodiments, a beam steering device in a castleconfiguration having one or more resistive high-side electrodes may bereferenced as a castle pro configuration herein.

An example system includes a first EO layer including an EO activematerial, and further including: a first number of active elements; asecond EO layer including the EO active material, and further includinga second number of active elements; a first high-side electrode layerincluding a first number of discrete electrodes, each of the firstnumber of discrete electrodes associated with one of the first number ofactive elements and positioned on a first side of the first EO layer; asecond high-side electrode layer including a second number of discreteelectrodes, each of the second number of discrete electrodes associatedwith one of the second number of active elements and positioned on afirst side of the second EO layer; and a low-side electrode arrangementsuch as: a first low-side electrode layer positioned on a second side ofthe first EO layer and a second low-side electrode layer positioned on asecond side of the second EO layer; a low-side electrode layerpositioned on a second side of the first EO layer and further positionedon a second side of the second EO layer; and a number of low-sideelectrodes, each positioned on a second side of the first EO layer or asecond side of the second EO layer. In the example system, each activeelement of the first number of active elements and the second number ofactive elements has an associated one of the number of low-sideelectrodes. The example system further includes where the first EO layerand the second EO layer are arranged such that the first number ofactive elements are not aligned with the second number of activeelements. For example, and without limitation, FIGS. 12-15 depictexample systems having such an arrangement.

An example system further includes: a first number of insulatingelements, each of the first number of insulating elements positionedbetween adjacent ones of the first number of active elements; a secondnumber of insulating elements, each of the second number of insulatingelements positioned between adjacent ones of the second number of activeelements; and/or an insulator layer operationally coupled to the secondEO layer, and having a number of insulating portions extending at leastpartially between each of the second number of active elements. Anexample system further includes: at least one additional EO layerincluding an additional number of active elements; at least oneadditional high-side electrode layer corresponding to each of the atleast one additional EO layers, each of the at least one additionalhigh-side electrode layers including an additional number of discreteelectrodes, each of the additional number of discrete electrodesassociated with one of the additional number of active elements andpositioned on a first side of the corresponding additional EO layer. Ina further example, the low-side electrode arrangement further includesone of: an additional low-side electrode layer or a number of additionallow-side discrete electrodes; such that each of the additional number ofactive elements is operationally coupled to a low-side electrode on asecond side of the corresponding additional EO layer. An example systemfurther includes a number of the additional EO layers, and may furtherinclude: where alternating adjacent pairs of the EO layers each shareone of the low-side electrode layers; where the first EO layer, thesecond EO layer, and the at least one additional EO layer are arrangedsuch that a perpendicular line through all of the EO layers passesthrough an equal thickness of active elements (and/or selected activeelements corresponding to intended steering elements for a particulartarget EM frequency or wavelength) of all of the EO layers; where thefirst EO layer, the second EO layer, and the at least one additional EOlayer are arranged such that a perpendicular line through all of the EOlayers passes through a configured thickness of the active elements(and/or selected active elements corresponding to intended steeringelements for a particular target EM frequency or wavelength) of all ofthe EO layers, the configured thickness including a thickness selectedto apply a progressive phase shift to an incident electro-magnetic (EM)beam; and/or where a terminating one of the first EO layer, the secondEO layer, or the at least one additional EO layer is associated with areflective low-side electrode layer.

In certain embodiments, EO active layers having alternating active cellsare referenced as a chess configuration herein. In certain embodiments,a chess configuration includes adjacent physical layers of the beamsteering device alternating such that an incident EM beam passes throughone or the other of the active cells from one of the EO active layers.In certain embodiments, a chess configuration includes active cells fromadjacent layers being sized the same (e.g., thickness, width, or both).In certain embodiments, a beam steering device in a chess configurationhaving one or more resistive high-side electrodes may be referenced as achess pro configuration herein.

Referencing FIG. 20, an example apparatus 1902 includes an incident beamcircuit 2002 that interprets an EM beam value 2004 (e.g., a wavelengthand/or frequency of an incident EM beam to a beam steering device), asteering request circuit 2006 that interprets a steering profile value2008, and a steering configuration circuit 1908 that determines a numberof voltage values 2010 in response to the steering profile value 2008.In certain embodiments, the steering request circuit 2006 determines thesteering profile value 2008 in response to the EM beam value 2004 and/ora steering request value 2012. An example steering profile value 2008includes steering instructions (e.g., wavelengths and/or polarities tobe steered, and a steering direction that may be determined in responseto a steering target location and/or a steering amount). An examplesteering configuration circuit 1908 determines the number of voltagevalues 2010 in response to the steering profile value 2008—for exampledetermining voltage values 2010 that provide configurations of activecells of a beam steering device to steer an incident EM beam in a mannerconsistent with the steering profile value 2008.

In certain embodiments, the number of voltage values 2010 correspond toa number of active cells of an EO material, where the number of voltagevalues 2010 include at least one progressive voltage value and a voltagereset value (e.g., a voltage trajectory across one or a number of activecells, and a voltage reset value that resets at each active cell and/orafter a selected number of active cells). The example apparatus 1902further includes a steering implementation circuit 1914 that provides anEO command value 1910 in response to the number of voltage values 2010.

Certain further aspects of an example apparatus are 1902 describedfollowing, any one or more of which may be present in certainembodiments. An example apparatus 1902 includes where the voltage resetvalue includes a voltage adjustment between two adjacent ones of thenumber of active cells to apply a 2πn phase shift between a first one ofthe adjacent ones of the active cells and a second one of the adjacentones of the of active cells, where n includes a small positive integervalue. An example steering profile value 2008 includes: a targetlocation for an EM beam; a target steering angle for an EM beam; a firsttarget steering angle for a first steering axis for an EM beam and asecond target steering angle for a second steering axis for the EM beam;and/or any of the foregoing for a selected polarity of the EM beam. Anexample EM beam value 2004 includes at least one EM beam value such as:a wavelength value of an incident EM beam, a presence of an incident EMbeam, and a characteristic of an incident EM beam (e.g., a polarity,energy level, timing value, incident angle, or the like). An exampleapparatus 1902 includes the steering configuration circuit 1908 furtherdetermining the number of voltage values 2010 for a number of layers ofactive cells of the EO material. In certain embodiments, the steeringimplementation circuit 1914 provides the EO command value(s) 1910 to adevice to implement the beam steering, for example to a steering controlmodule 1916.

The following descriptions reference schematic flow diagrams andschematic flow descriptions for certain procedures and operationsaccording to the present disclosure. Any such procedures and operationsmay be utilized with and/or performed by any systems of the presentdisclosure, and with other procedures and operations describedthroughout the present disclosure. Any groupings and ordering ofoperations are for convenience and clarity of description, andoperations described may be omitted, re-ordered, grouped, and/ordivided, in whole or part, unless explicitly indicated otherwise.

Referencing FIG. 21, an example procedure 2100 includes an operation2102 to receive an incident electro-magnetic (EM) beam at a multi-layerbeam steering device, an operation 2104 to determine a wavelength valueof the incident EM beam, and an operation 2106 to selectively steer theEM beam with a first layer or a second layer of the multi-layer beamsteering device in response to the determined wavelength value of theincident EM beam.

Certain further aspects of an example procedure are described following,any one or more of which may be present in certain embodiments. Anexample procedure further includes the operation 2106 to selectivelysteer by: applying selected voltages to a selected one of the firstlayer or the second layer, applying a voltage gradient across theselected one of the first layer or the second layer, and/or by applyingresets at selected intervals across the selected one of the first layeror the second layer. An example procedure further includes an operation2108 to determine a selection frequency of interest, and an operation2110 to alternate the wavelength value of the incident EM beam at afrequency at least equal to the selection frequency of interest.

Referencing FIG. 22, an example procedure 2200 includes an operation2102 to receive an incident electro-magnetic (EM) beam at a number ofactive cells of an electro-optic (EO) material; an operation 2202 toapply a voltage to the number of active cells, thereby selectivelyadjusting an optical characteristic of each of the number of activecells; and an operation 2204 to reset a voltage between at least twoadjacent ones of the number of active cells, thereby steering theincident EM beam. In certain embodiments, the number of active cellsbetween reset operations 2204 is a single active cell—for example whereresistive high-side electrodes, tilted electrodes, and/or otherconfigurations described throughout the present disclosure provide for aconfiguration where a voltage gradient can be applied across a singleactive cell. In certain embodiments, even where a voltage gradient canbe applied across a single active cell, the operation 2204 to reset thevoltage may be performed after a number of active cells greater than one(1) cell, for example, where a voltage gradient is continued into asecond cell (e.g., to reduce the number of resets across the beamsteering device, to keep a voltage gradient across a single cell below aselected value, to keep a voltage gradient across a single cell within alinear or other selected region for a conductive resistor, etc.).

Certain further aspects of an example procedure 2200 are describedfollowing, any one or more of which may be present in certainembodiments. An example procedure includes the operation 2204 to resetthe voltage including one or more of: resetting the voltage by an amountto apply a 2π phase shift between a first one of the number of activecells and an adjacent second one of the number of active cells;resetting the voltage by an amount to apply a 2πn phase shift between afirst one of the number of active cells and an adjacent second one ofthe number of active cells, where n includes a small positive integervalue; and/or resetting the voltage to a value applying a negative phaseshift. An example procedure 2200 further includes operation 2202 toapply the voltage to the number of active cells to: apply a progressivephase shift to the incident EM beam; and/or to apply the progressivephase shift by applying progressive voltages to adjacent ones of thenumber of active cells, and resetting the progressive voltages atselected intervals of the number of active cells. In certainembodiments, the selected intervals of the number of active cellsbetween resets include at least six (6) of the number of active cells ineach of the selected intervals. In certain embodiments, operation 2202to apply the voltage to the number of active cells includes: applying auniform voltage to each of the number of active cells, and furtherapplying a distinct uniform voltage to adjacent ones of the number ofactive cells; applying a voltage gradient to each of the number ofactive cells; and/or applying a distinct voltage gradient to adjacentones of the number of active cells.

An example procedure 2200 further includes an operation 2206 to insulatea first high side electrode corresponding to a first one of the numberof active cells from a second high side electrode corresponding to asecond one of the number of active cells, where the first one of thenumber of active cells is adjacent to the second one of the number ofactive cells. In certain embodiments, the operation 2206 includesenhancing the insulating in response to the first one of the number ofactive cells and the second one of the active cells including the atleast two of the number of active cells corresponding to the resettingthe voltage (e.g., providing enhanced insulating between a final activecell of a first progressive phase delay stage having a maximum phaseshift/voltage, and an initial active cell a second progressive phasedelay stage having a minimum phase shift/voltage). An example procedure2200 further includes an operation 2208 to steer the incident EM beam ina first axis, thereby providing a first axis steered EM beam. In certainembodiments, the procedure 2200 further includes an operation 2210 todetermine whether additional axes and/or additional polarities of theincident EM beam are to be steered, and to repeat operations 2102, 2202,2204, and 2206, thereby steering the in a second axis and/or a secondpolarity. For example, procedure 2200 further includes, in response tooperation 2210 determining YES, an operation 2102 to receive the firststeered EM beam (e.g., from a previous iteration of procedure 2200) at asecond number of active cells of the EO material, an operation 2202 toapply a voltage to the second number of active cells, therebyselectively adjusting an optical characteristic of each of the secondnumber of active cells; and/or an operation 2204 to reset a voltagebetween at least two adjacent ones of the second number of active cells,thereby steering the incident EM beam in a second axis (and/or secondpolarity) distinct from the first axis (and/or first polarity). Incertain embodiments, procedure 2200 further includes an operation 2206to insulate a first high side electrode corresponding to a first one ofthe second number of active cells from a second high side electrodecorresponding to a second one of the second number of active cells,where the first one of the second number of active cells is adjacent tothe second one of the second number of active cells. It can be seen thatthe operations of the example procedure 2200 provide a two-axis steeredand/or two-polarity steered EM beam.

Referencing FIG. 23, an example procedure 2300 includes an operation2302 to interpret an electro-magnetic (EM) beam value, an operation 2304to interpret a steering profile value, and an operation 2306 todetermine a number of voltage values in response to the steering profilevalue. The number of voltage values correspond to a number of activecells of an EO material, and the number of voltage values include atleast one progressive voltage value and a voltage reset value. Incertain embodiments, progressive voltage values may be within an activecell, and/or stepped between active cells. The example procedure 2300further includes an operation 2308 to provide an EO command value inresponse to the number of voltage values.

Certain further aspects of an example procedure are described following,any one or more of which may be present in certain embodiments. Anexample procedure 2300 further includes: where the voltage reset valueincludes a voltage adjustment between two adjacent ones of the number ofactive cells to apply a 2πn phase shift between a first one of theadjacent ones of the active cells and a second one of the adjacent onesof the of active cells, where n includes a small positive integer value.An example steering profile value includes a target location for an EMbeam and/or a target steering angle for the EM beam; where the steeringprofile value includes a first target steering angle for a firststeering axis for an EM beam and a second target steering angle for asecond steering axis for the EM beam; where the steering profile valueincludes a first target steering angle for a first polarity of the EMbeam and a second target steering angle for a second polarity of the EMbeam; and/or where the EM beam value includes at least one EM beam valuesuch as: a wavelength value of an incident EM beam, a presence of anincident EM beam, and a characteristic of an incident EM beam. Anexample procedure 2300 further includes the operation 2306 to determinethe number of voltage values for a number of layers of active cells ofthe EO material.

Referencing FIG. 24, an example procedure 2400 includes an operation2402 to provide an EO layer including an EO active material, and anoperation 2404 to form a number of active cells of the EO layer, wherethe forming includes: operationally coupling a high-side electrode layerincluding a number of discrete electrodes to a first side of the EOlayer; and operationally coupling a low-side electrode layer to a secondside of the EO layer. The example procedure 2400 further includes anoperation 2406 to operationally couple an insulator to the number ofactive cells of the EO layer, where the insulator is at least partiallypositioned between a first one of the active cells and a second one ofthe active cells.

Certain further aspects of an example procedure 2400 are describedfollowing, any one or more of which may be present in certainembodiments. An example procedure 2400 further includes: operation 2402including providing the EO layer in a castle configuration; operation2402 including providing a number of EO layers in a chess configuration;operation 2404 including operationally coupling the high-side electrodelayer by providing the number of discrete electrodes as resistiveelectrodes; operation 2404 including operationally coupling thehigh-side electrode layer by providing the number of discrete electrodesas tilted electrodes; and/or operation 2404 including operationallycoupling the high-side electrode layer by providing the number ofdiscrete electrodes as electrodes having a selected geometricarrangement. An example procedure 2400 further includes: operation 2402including providing the EO layer by providing a number of EO layers, andoperation 2404 further including forming the number of active cells ofthe EO layer by operationally coupling each one of a number of high-sideelectrode layers to a corresponding one of the number of EO layers;and/or operation 2404 further including forming the number of activecells of the EO layer by operationally coupling a low-side electrodelayer such that the low-side electrode layer is shared by adjacent onesof the number of EO layers. An example procedure 2400 further includes:operation 2402 further including providing the EO layer by utilizing acontiguous substrate of the EO material for the EO layer; operation 2406further including operationally coupling the insulator by utilizing acontiguous substrate of insulator material for the insulator; operation2404 further including operationally coupling the low-side electrodelayer by utilizing a reflective low-side electrode layer; operation 2404further including operationally coupling the high-side electrode layerby providing the number of discrete electrodes as resistive electrodeshaving a selectable resistance profile; and/or operation 2404 furtherincluding providing the number of discrete electrodes as resistiveelectrodes having a selectable resistance profile by providing thenumber of discrete electrodes as solid state electrodes.

Referencing FIG. 25, an example procedure 2500 for implementing animproved modulo 2πn electro-optical or photonic beam steering scannerincludes an operation 2502 to provide a modulo 2πn electro-optical orphotonic beam steering scanner, an operation 2504 to introducing a beamof light to at least one active EO crystal layer of the scanner, and anoperation 2506 to impose one or more voltages on conductive or resistivediscrete electrodes of the scanner to change an index of refractionsufficient to cause an OPD change to the beam of light traveling throughthe scanner.

Without limitation to any other aspect of the present disclosure; afirst example improved modulo 2πn electro-optical or photonic beamsteering scanner usable with procedure 2500 includes at least one activeEO layer having a first side and an opposing second side; at least oneconductive or resistive discrete electrode, arranged along the firstside; at least one ground electrode arranged along the second side, andat least one insulator arranged to extend at least partially into theactive EO layer; and a second example improved modulo 2πnelectro-optical or photonic beam steering scanner usable with procedure2500 includes at least two active rows arranged between two substrates,the substrates transparent to an incoming optical or photonic wave, eachactive row having a first side and an opposing second side, where eachactive row includes at least two active cells separated by at least oneinsulator cell, at least one ground electrode arranged between two ofthe at least two active rows; each of the at least two active rowshaving at least one discrete conductive or resistive electrode arrangedalong the first side or second side of each active row opposite the atleast one ground electrode; and where an arrangement of the at least twoactive cells and insulator cells in one of the at least two active rowsis opposite to the arrangement of the at least two active cells andinsulator cells in the other of the at least two active rows.

Certain aspects of the present disclosure are set forth as a means forsteering an incident EM beam on a beam steering device withoutmechanically moving parts. Without limitation to any other aspect of thepresent disclosure, certain examples of a means for steering an incidentEM beam on a beam steering device without mechanically moving parts aredescribed following. An example system includes a number of active cellsof an EO active material formed between a number of discrete high-sideelectrodes and low-side electrode(s), where the low-side electrodes maybe continuous, discrete, or a combination of those. The example systemfurther includes the high-side electrodes being either conductive,resistive, or a combination of those. The example system furtherincludes insulating elements positioned at least partially betweenadjacent active cells, and/or further includes insulating elementsconfigured with insulation capability configured for a voltagedifferential between the adjacent active cells. Example and non-limitinginsulating elements include: electrically insulating materials,geometric arrangements that provide for distance between adjacenthigh-side electrodes (e.g., a castle and/or a chess arrangement), adielectric material, and/or an air gap. An example system includeshigh-side electrodes that have one or more of the following features: aconfigurable conductivity/resistance profile, and/or a tilt or othergeometric progression across one or more of the active cells. An examplesystem includes a number of layers of EO active material, where eachlayer is configured to steer an incident EM beam, and/or where two ormore layers cooperate together to steer the incident EM beam. An examplesystem includes the EO active material including one or more of: EOcrystals, liquid crystals, and/or quantum dot materials; and/or wherethe EO crystals include a material such as PMN-PT, KTN, SBN, PBN, PZT,and/or BaTiO₃. An example system includes a reflective layer provided ona low-side electrode layer and/or on a substrate layer. An examplesystem includes real-time control of the voltages of the high-sideelectrodes, thereby steering the EM beam to a selected angle, and/orcontrolling one or more selected ones of an axis of steering, a polarityof steering, and/or steering a wavelength of interest. An example systemincludes active cells of the EO active material having a thickness of ½λ, λ, not greater than 2λ, not greater than 5λ, not greater than OX,and/or not greater than 100λ, where λ corresponds to wavelength ofinterest for a selected EM beam to be steered. An example systemincludes one or more of an insulator, an electrode (high-side and/orlow-side), a substrate, and/or an active EO material having a similaroptical characteristic. An example system includes providing a phasedelay progression across one or more active cells of the EO activelayer, and resetting the phase delay progression at selected activecells of the EO active layer. An example system includes resetting thephase delay progression by a value of about 2πn. An example systemincludes resetting the phase delay progression to a value of zero phasedelay, to a value of about zero phase delay, and/or to a value below azero phase delay. An example system includes providing a number of stepsin the phase delay progression stage to improve a quantization steeringefficiency of the beam steering device. An example system includesutilizing selected flyback effects in a staged beam steering device tosmooth the phase delay profile of the beam steering device.

Certain aspects of the present disclosure are set forth as a means forsteering an incident EM beam in two distinct axes. Without limitation toany other aspect of the present disclosure, certain examples of a meansfor steering an incident EM beam in two distinct axes are describedfollowing. An example system includes steering the incident EM beam in afirst axis with a first active EO layer, and steering the incident EMbeam in a second axis with a second active EO layer. An example systemincludes either one or both of the first active EO layer and the secondactive EO layer being distributed across more than one physical layer ofactive cells. An example system includes active cells of the firstactive EO layer sharing a physical layer of active cells with activecells of the second active EO layer. An example system includes a meansfor steering the incident EM beam in two distinct polarities in asimilar manner to means for steering the incident EM beam in twodistinct axes.

Certain aspects of the present disclosure are set forth as a means forsteering at least two incident EM beams having distinct wavelengths.Without limitation to any other aspect of the present disclosure,certain examples of a means for steering at least two incident EM beamshaving distinct wavelengths are described following. An example systemincludes a first active EO layer configured to steer a first wavelength,and a second active EO layer configured to steer a second wavelength,and a controller that operates voltages provided to high-side electrodesof the first active EO layer and the second active EO layer such thatthe selected wavelength is steered, and the not selected wavelength isnot steered. An example system includes an active EO layer capable tosteer more than one distinct wavelength—for example where the distinctwavelengths have λ values in an integer ratio of each other.

Certain aspects of the present disclosure are set forth as a means forsteering an incident EM beam at a steering efficiency exceeding 90%.Without limitation to any other aspect of the present disclosure,certain examples of a means for steering an incident EM beam at asteering efficiency exceeding 90% are described following. An examplesystem includes a beam steering device having resistive, tilted, and/orgeometrically arranged high-side electrodes sufficient to reducequantization losses and thereby support a 90% steering efficiency. Anexample system includes a beam steering device having insulatingelements positioned at least partially between adjacent active cells,and/or further includes insulating elements configured with insulationcapability configured for a voltage differential between the adjacentactive cells sufficient to reduce flyback losses and thereby support a90% steering efficiency. Example and non-limiting insulating elementsinclude: electrically insulating materials, geometric arrangements thatprovide for distance between adjacent high-side electrodes (e.g., acastle and/or a chess arrangement), a dielectric material, and/or an airgap. An example system includes one or more of an insulator, anelectrode (high-side and/or low-side), a substrate, and/or an active EOmaterial having a similar optical characteristic sufficient to reduceredirection losses and thereby support a 90% steering efficiency. Anexample system includes an anti-reflective material at a materialdiscontinuity in the beam steering device, sufficient to reduceredirection losses and thereby support a 90% steering efficiency.

Certain aspects of the present disclosure are set forth as a means forsteering an incident EM beam at a steering efficiency exceeding 95%.Without limitation to any other aspect of the present disclosure,certain examples of a means for steering an incident EM beam at asteering efficiency exceeding 95% are described following. An examplesystem includes a beam steering device having resistive, tilted, and/orgeometrically arranged high-side electrodes sufficient to reducequantization losses and thereby support a 95% steering efficiency. Anexample system includes a beam steering device having insulatingelements positioned at least partially between adjacent active cells,and/or further includes insulating elements configured with insulationcapability configured for a voltage differential between the adjacentactive cells sufficient to reduce flyback losses and thereby support a95% steering efficiency. Example and non-limiting insulating elementsinclude: electrically insulating materials, geometric arrangements thatprovide for distance between adjacent high-side electrodes (e.g., acastle and/or a chess arrangement), a dielectric material, and/or an airgap. An example system includes one or more of an insulator, anelectrode (high-side and/or low-side), a substrate, and/or an active EOmaterial having a similar optical characteristic sufficient to reduceredirection losses and thereby support a 95% steering efficiency. Anexample system includes an anti-reflective material at a materialdiscontinuity in the beam steering device, sufficient to reduceredirection losses and thereby support a 95% steering efficiency.

The present disclosure teaches a number of systems and techniques forcreating and using a high diffraction efficiency modulo 2πn optical beamscanner. In certain embodiments, a scanner includes at least twooptically active rows interposed between two substrates with an optionalreflective layer as the last layer. Each optically active row containsat least two active cells made of an electro optically active materialwhose index of refraction or other optical characteristics can bedynamically changed in one, or both, polarizations. The active cells arearranged between two electrode layers. One electrode layer can beground, and at least one layer may have one or more voltages applied.The electrodes can be transparent to an incoming optical wave, and/orhave selected transmissivity to selected electro-magnetic (EM)frequencies, and can be conductive or resistive. In certain embodiments,adjacent active cells are at least partially separated by an insulator.Example insulators and substrates are made of a material with the sameor a similar index of refraction, and/or are transparent (and/or haveselected transmissivity to selected EM frequencies) to the incomingoptical or photonic wave intended for deflection by the scanner.

An example system includes a high-side electrode layer having a numberof discrete electrodes, a low-side electrode layer, and an electro-optic(EO) layer including an EO active material at least partially positionedbetween the high-side electrode layer and the low-side electrode layer,thereby forming a number of active cells of the EO layer. Each of thenumber of active cells of the EO layer includes a portion of the EOlayer positioned between 1) a first one of the number of discreteelectrodes of the high-side electrode layer, and 2) the low-sideelectrode layer. The example system includes an insulator operationallycoupled to the active cells of the EO layer, and at least partiallypositioned between a first one of the active cells and a second one ofthe active cells.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes: where the EO layer includes at least six (6)active cells, where the system further includes a number of theinsulators, and where each of the number of insulators is positionedbetween two of the at least six (6) active cells; where the EO layerincludes at least eight (8) active cells, the system further including anumber of the insulators, and where each of the number of insulators ispositioned between two of the at least eight (8) active cells; where theEO layer includes between three (3) active cells and twenty (20) activecells, inclusive; and/or where the system further includes a number ofthe insulators, and where each of the number of insulators is positionedbetween two of the active cells. An example system includes: where atleast one of the number of discrete electrodes includes a conductiveelectrode; where at least one of the number of discrete electrodesincludes a resistive electrode; where a selected number of the activecells of the EO layer are structured to apply a progressive phase shiftto an incident electro-magnetic (EM) beam; and/or where a next one ofthe active cells of the EO layer after the selected number of activecells is configured to reset the progressive phase shift of the incidentEM beam by reducing the progressive phase shift by 2π, and/or by 2πn,where n can be a relatively small positive integer value. An examplesystem includes where a last one of the selected number of active cellsincludes a phase shift such as: a value between 1.5πn and 2.5πn, a valuebetween 1.8πn and 2.2πn, a value between 1.9πn and 2.05πn, a value ofabout 2πn, and a value of 2πn. In certain embodiments, n includes avalue between 1 and 10, inclusive. An example system includes where eachof the number of insulators includes at least one of a size or aresistivity selected in response to a voltage difference value of thecorresponding active cells of the EO layer; and/or where each one of thenumber of insulators positioned between a last one of the selectednumber of active cells and the next one of the active cells is a resetinsulator, and where the reset insulator includes at least one of anincreased insulation area or an increased resistivity value. An examplesystem includes where the EO layer has a thickness of at least onewavelength corresponding to a target electro-magnetic (EM) frequency;and/or where the EO layer includes a progressive thickness value, wherea thickest portion of the progressive thickness value includes athickness of at least one wavelength corresponding to a targetelectro-magnetic (EM) frequency. An example system includes the EO layerincluding at least one material such as: an EO crystal, a crystal layer,multiple crystal layers, an EO crystal layer, multiple EO crystallayers, a liquid crystal, a polymer, a quantum dot device, a crystalthat responds to an applied electric field with a linear change in anindex of refraction, and/or a crystal that responds to an appliedelectric field with a quadratic change in an index of refraction.

An example system includes where the high-side electrode layer, thelow-side electrode layer, and the EO layer together make up a firstphase delay progression stage, and where the system further includes asecond phase delay progression stage. The second phase delay progressionstage includes: a second high-side electrode layer including a number ofdiscrete electrodes; a second low-side electrode layer; a second EOlayer including an EO active material at least partially interposedbetween the second high-side electrode layer and the second low-sideelectrode layer, thereby forming a number of active cells of the secondEO layer. Each of the number of active cells of the second EO layerincludes a portion of the second EO layer positioned between 1) a firstone of the number of discrete electrodes of the second high-sideelectrode layer; and 2) the second low-side electrode layer. The examplesystem further includes a second insulator operationally coupled to theactive cells of the second EO layer, and at least partially positionedbetween a first one of the active cells and a second one of the activecells. In certain further aspects, an example system includes where thefirst phase delay progression stage and the second phase delayprogression stage are configured to additively steer an incidentelectro-magnetic (EM) beam; where the first phase delay progressionstage is configured to steer an incident electro-magnetic (EM) beamalong a first axis, and where the second phase delay progression stageis configured to steer the incident EM beam along a second axis, andwhere the first axis is distinct from the second axis, and/or where thefirst axis is perpendicular to the second axis; where the first axiscorresponds to a first polarization of the incident EM beam, and wherethe second axis corresponds to a second polarization of the incident EMbeam; and/or the system further including a half wave plate layerinterposed between the first phase delay progression stage and thesecond phase delay progression stage, where the half wave plate layer isstructured to selectively rotate a polarization of the incident EM beam.An example system includes where the low-side electrode layer includes acontinuous electrode, where the low-side electrode layer includes aground voltage electrode; and/or where the ground voltage electrodeincludes a zero relative voltage electrode.

An example system includes a high-side electrode layer including anumber of discrete conductive electrodes, a low-side electrode layer,and an EO layer including an EO active material at least partiallypositioned between the high-side electrode layer and the low-sideelectrode layer, thereby forming a number of active cells of the EOlayer. Each of the number of active cells of the EO layer includes aportion of the EO layer positioned between 1) a first one of the numberof discrete electrodes of the high-side electrode layer, and 2) thelow-side electrode layer. The example system further includes aninsulator operationally coupled to the active cells of the EO layer, andat least partially positioned between a first one of the active cellsand a second one of the active cells.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes where the EO layer includes at least eight (8)active cells, where the system further includes a number of theinsulators, and where each of the number of insulators is positionedbetween two of the at least eight (8) active cells. An example systemincludes where the EO layer includes a number of active cells, thenumber of active cells including at least a number of cells such as:eight (8), ten (10), twelve (12), sixteen (16), and twenty (20), wherethe system further includes a number of the insulators, and where eachof the number of insulators is positioned between two of the activecells. An example system includes: where a selected number of the activecells of the EO layer are structured to apply a progressive phase shiftto an incident electro-magnetic (EM) beam; where a next one of theactive cells of the EO layer after the selected number of active cellsis configured to reset the progressive phase shift of the incident EMbeam by reducing the progressive phase shift by 2π; where a last one ofthe selected number of active cells includes a phase shift selected suchas: a value between 1.5π and 2.5π, a value between 1.8π and 2.2π, avalue between 1.9π and 2.05π, a value of about 2π, and a value of 2π;where a next one of the active cells of the EO layer after the selectednumber of active cells is configured to reset the progressive phaseshift of the incident EM beam by reducing the progressive phase shift by2πn, where n includes a small positive integer value; and/or where nincludes a value between 1 and 10 inclusive. An example system includes:where each of the number of insulators includes at least one of a sizeor a resistivity selected in response to a voltage difference value ofthe corresponding active cells of the EO layer; where each one of thenumber of insulators positioned between a last one of the selectednumber of active cells and the next one of the active cells includes areset insulator, and where the reset insulator includes at least one ofan increased insulation area or an increased resistivity value; wherethe EO layer includes a thickness of at least one wavelengthcorresponding to a target electro-magnetic (EM) frequency; where the EOlayer includes a progressive thickness value, where a thickest portionof the progressive thickness value includes a thickness of at least onewavelength corresponding to a target electro-magnetic (EM) frequency;and/or where the EO layer includes at least one material such as: an EOcrystal, a crystal layer, multiple crystal layers, an EO crystal layer,multiple EO crystal layers, a liquid crystal, a polymer, a quantum dotdevice, a crystal that responds to an applied electric field with alinear change in an index of refraction, and/or a crystal that respondsto an applied electric field with a quadratic change in an index ofrefraction.

An example system includes a high-side electrode layer including anumber of discrete resistive electrodes, a low-side electrode layer, andan EO layer including an EO active material at least partiallypositioned between the high-side electrode layer and the low-sideelectrode layer, thereby forming a number of active cells of the EOlayer. The example system includes each of the number of active cells ofthe EO layer including a portion of the EO layer positioned between 1) afirst one of the number of discrete electrodes of the high-sideelectrode layer, and 2) the low-side electrode layer. The example systemfurther includes an insulator operationally coupled to the active cellsof the EO layer, and at least partially positioned between a first oneof the active cells and a second one of the active cells.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes where the active cells of the EO layer arestructured to apply a voltage gradient across the active cell; where anext active cell of the EO layer is configured to reset the voltagerelative to the previous active cell of the EO layer to reset anincident electro-magnetic (EM) beam by a 2π phase shift; where a highestvoltage of the voltage gradient is configured to provide a phase shiftof the EM beam by a phase shift such as: a value between 1.5π and 2.5π,a value between 1.8π and 2.2π, a value between 1.9π and 2.05π, a valueof about 2π, and a value of 2π; where a next active cell of the EO layeris configured to reset the voltage relative to the previous active cellof the EO layer to reset an incident electro-magnetic (EM) beam by 2πn,where n includes a small positive integer value; and/or where n includesa value between 1 and 10 inclusive. An example system includes where aselected number of the number of the active cells of the EO layer areconfigured to provide a voltage gradient across the number of the activecells; where a next active cell of the EO layer is configured to resetthe voltage relative to a last one of the selected number of the numberof active cells of the EO layer to reset an incident electro-magnetic(EM) beam by a 2π phase shift; where a last one of the selected numberof active cells includes a phase shift such as: a value between 1.5π and2.5π, a value between 1.8π and 2.2π, a value between 1.9π and 2.05π, avalue of about 2π, and a value of 2π; where the next active cell of theEO layer after the selected number of active cells is configured toreset the progressive phase shift of the incident EM beam by reducingthe progressive phase shift by 2πn, where n includes a small positiveinteger value; and/or where n includes a value between 1 and 10inclusive. An example system includes where each of the number ofinsulators includes at least one of a size or a resistivity selected inresponse to a voltage difference value of the corresponding active cellsof the EO layer, and/or where each one of the number of insulatorspositioned between a last one of the selected number of active cells andthe next active cell includes a reset insulator, and where the resetinsulator includes at least one of an increased insulation area or anincreased resistivity value.

An example system includes a first phase delay progression stage,including: a first high-side electrode layer including a first number ofdiscrete electrodes; a first low-side electrode layer; a first EO layerincluding an EO active material at least partially positioned betweenthe first high-side electrode layer and the first low-side electrodelayer, thereby forming a number of active cells of the first EO layer.Each of the number of active cells of the first EO layer includes aportion of the first EO layer positioned between 1) a first one of thefirst number of discrete electrodes of the first high-side electrodelayer, and 2) the first low-side electrode layer. The example systemfurther includes a first insulator operationally coupled to the activecells of the first EO layer, and at least partially positioned between afirst one of the active cells and a second one of the active cells. Theexample system further includes a second phase delay progression stage,including: a second high-side electrode layer including a second numberof discrete electrodes; a second low-side electrode layer; a second EOlayer including an EO active material at least partially positionedbetween the second high-side electrode layer and the second low-sideelectrode layer, thereby forming a number of active cells of the secondEO layer. Each of the number of active cells of the second EO layerincludes a portion of the second EO layer positioned between 1) a firstone of the second number of discrete electrodes of the second high-sideelectrode layer, and 2) the second low-side electrode layer. The examplesystem further includes a second insulator operationally coupled to theactive cells of the second EO layer, and at least partially positionedbetween a first one of the active cells and a second one of the activecells.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes where the first EO layer includes a firstthickness corresponding to a thickness of at least one wavelengthcorresponding to a first target electro-magnetic (EM) frequency, andwhere the second EO layer includes a second thickness corresponding to athickness of at least one wavelength corresponding to a second target EMfrequency. An example system includes a controller, the controllerincluding an incident wavelength circuit that determines a wavelengthvalue of an incident EM beam, a steering configuration circuit thatdetermines a first EO layer command value and a second EO layer commandvalue in response to the incident EM beam, and a steering implementationcircuit that provides at least one of the first EO layer command valueor the second EO layer command value to a steering control module. Anexample steering control module provides selected voltages to at leastone of the first high-side electrode layer or the second high-sideelectrode layer in response to the at least one of the first EO layercommand value or the second EO layer command value. An example steeringcontrol module further includes a solid state circuit that appliesselected voltages to each electrode of the first high-side electrodelayer and the second high-side electrode layer. An example solid statecircuit further selectively couples a power source to each electrode ofthe first high-side electrode layer and the second high-side electrodelayer, and/or selectively couples the power source using a pulse-widthmodulation (PWM) operation.

An example procedure includes an operation to receive an incidentelectro-magnetic (EM) beam at a multi-layer beam steering device, anoperation to determine a wavelength value of the incident EM beam, andan operation to selectively steer the EM beam with a first layer or asecond layer of the multi-layer beam steering device in response to thedetermined wavelength value of the incident EM beam.

Certain further aspects of an example procedure are described following,any one or more of which may be present in certain embodiments. Anexample procedure further includes selectively steering by applyingselected voltages to a selected one of the first layer or the secondlayer; selectively steering further by applying a voltage gradientacross the selected one of the first layer or the second layer; and/orselectively steering by applying resets at selected intervals across theselected one of the first layer or the second layer. An exampleprocedure further includes an operation to determine a selectionfrequency of interest, and to alternate the wavelength value of theincident EM beam at a frequency at least equal to the selectionfrequency of interest.

An example system includes a high-side electrode layer including anumber of discrete electrodes, a low-side electrode layer, where thelow-side electrode layer includes a reflective layer, and an EO layerincluding an EO active material at least partially interposed betweenthe high-side electrode layer and the low-side electrode layer, therebyforming a number of active cells of the EO layer; where each of thenumber of active cells of the EO layer includes a portion of the EOlayer positioned between 1) a first one of the number of discreteelectrodes of the high-side electrode layer, and 2) the low-sideelectrode layer. The example system further includes an insulatoroperationally coupled to the active cells of the EO layer, and at leastpartially positioned between a first one of the active cells and asecond one of the active cells.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes the EO layer including at least eight (8) activecells, the system further including a number of the insulators, andwhere each of the number of insulators is positioned between two of theat least eight (8) active cells; where at least one of the number ofdiscrete electrodes includes a conductive electrode; where at least oneof the number of discrete electrodes includes a resistive electrode;where a selected number of the active cells of the EO layer arestructured to apply a progressive phase shift to an incidentelectro-magnetic (EM) beam; where a next one of the active cells of theEO layer after the selected number of active cells is configured toreset the progressive phase shift of the incident EM beam by reducingthe progressive phase shift by 2π; where a last one of the selectednumber of active cells includes a phase shift selected from the phaseshifts consisting of: a value between 1.5π and 2.5π, a value between1.8π and 2.2π, a value between 1.9π and 2.05π, a value of about 2π, anda value of 2π; where a next one of the active cells of the EO layerafter the selected number of active cells is configured to reset theprogressive phase shift of the incident EM beam by reducing theprogressive phase shift by 2πn, where n includes a small positiveinteger value; and/or where n includes a value between 1 and 10inclusive. An example system includes where each of the number ofinsulators includes at least one of a size or a resistivity selected inresponse to a voltage difference value of the corresponding active cellsof the EO layer; and/or where each one of the number of insulatorspositioned between a last one of the selected number of active cells andthe next one of the active cells includes a reset insulator, and wherethe reset insulator includes at least one of an increased insulationarea or an increased resistivity value. An example system includes theEO layer having a thickness of at least one wavelength corresponding toa target electro-magnetic (EM) frequency; where the EO layer includes aprogressive thickness value, and where a thickest portion of theprogressive thickness value includes a thickness of at least onewavelength corresponding to a target electro-magnetic (EM) frequency;and/or where the EO layer includes at least one material such as: an EOcrystal, a crystal layer, multiple crystal layers, an EO crystal layer,multiple EO crystal layers, a liquid crystal, a polymer, a quantum dotdevice, a crystal that responds to an applied electric field with alinear change in an index of refraction, and/or a crystal that respondsto an applied electric field with a quadratic change in an index ofrefraction.

An example system further includes the high-side electrode layer, thelow-side electrode layer, and the EO layer together making up a firstphase delay progression stage, and where the system further includes asecond phase delay progression stage. The second phase delay progressionstage includes: a second high-side electrode layer including a number ofdiscrete electrodes, a second low-side electrode layer, and a second EOlayer including an EO active material at least partially positionedbetween the second high-side electrode layer and the second low-sideelectrode layer, thereby forming a number of active cells of the secondEO layer. The example system further includes each of the number ofactive cells of the second EO layer including a portion of the second EOlayer positioned between 1) a first one of the number of discreteelectrodes of the second high-side electrode layer, and 2) the secondlow-side electrode layer. The example system further includes a secondinsulator operationally coupled to the active cells of the second EOlayer, and at least partially positioned between a first one of theactive cells and a second one of the active cells. In certainembodiments, the example system further includes: where the first phasedelay progression stage and the second phase delay progression stage areconfigured to additively steer an incident electro-magnetic (EM) beam;where the first phase delay progression stage is configured to steer anincident electro-magnetic (EM) beam along a first axis, where the secondphase delay progression stage is configured to steer the incident EMbeam along a second axis, and where the first axis is distinct from thesecond axis; and/or where the first axis is perpendicular to the secondaxis. An example system further includes: where the first axiscorresponds to a first polarization of the incident EM beam, and wherethe second axis corresponds to a second polarization of the incident EMbeam; and/or a half wave plate layer interposed between the first phasedelay progression stage and the second phase delay progression stage,where the half wave plate layer is structured to selectively rotate apolarization of the incident EM beam. An example system further includeswhere the low-side electrode layer includes a continuous electrode;where the low-side electrode layer includes a ground voltage electrode;and/or where the ground voltage electrode includes a zero relativevoltage electrode.

An example system includes an EO substrate layer including an EO activematerial and further including a number of thin elements alternatingwith a number of thick elements, a high-side electrode layer including anumber of discrete electrodes, each of the number of discrete electrodesassociated with one of the number of thick elements and positioned on afirst side of the EO substrate layer, and a low-side electrode layerpositioned on a second side of the EO substrate layer. The examplesystem further includes an insulator layer operationally coupled to theEO substrate layer, and at least partially positioned between each ofthe number of thick elements.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system further includes: where the high-side electrode layerfurther includes a second number of discrete electrodes, each of thesecond number of discrete electrodes associated with one of the numberof thin elements; where each of the number of thick elements includes anidentical thickness; where each of the number of thin elements includesan identical thickness; where each of the number of thin elementsincludes a thickness of one wavelength corresponding to a targetelectro-magnetic (EM) frequency; and/or where each of the number ofthick elements includes a thickness of two wavelengths corresponding tothe target EM frequency. An example system further includes: a second EOsubstrate layer including a second number of thin elements alternatingwith a second number of thick elements, and where the EO substrate layerand the second EO substrate layer are aligned such that the number ofthick elements is not aligned with the second number of thick elements;a second high-side electrode layer including a second number of discreteelectrodes, each of the second number of discrete electrodes associatedwith one of the second number of thick elements, and positioned on afirst side of the second EO substrate layer; and/or where the EOsubstrate layer and the second EO substrate layer share the groundelectrode. An example system includes: where each of the number ofdiscrete electrodes comprise resistive electrodes; a number of the EOsubstrate layers, where each of the number of EO substrate layers have acorresponding high-side electrode layer, and where the number of EOsubstrate layers are aligned such that a perpendicular line through thenumber of the EO substrate layers intersects only one of the number ofthick elements of the number of the EO substrate layers; a number of theEO substrate layers, and where the number of EO substrate layers arearranged such that a perpendicular line through the number of the EOsubstrate layers passes through an equal thickness of active elements ofthe number of the EO substrate layers; where each high-side electrodelayer further includes a second number of discrete electrodes, each ofthe second number of discrete electrodes associated with one of thenumber of thin elements of the number of EO substrate layers; and/orwhere the active elements include each of the number of thin elementsand each of the number of thick elements having an associated discreteelectrode. An example system includes: a number of the EO substratelayers, and where the number of EO substrate layers are arranged suchthat a perpendicular line through the number of the EO substrate layerspasses through a configured thickness of the active elements of thenumber of the EO substrate layers, the configured thickness including athickness selected to apply a progressive phase shift to an incidentelectro-magnetic (EM) beam; where each high-side electrode layer furtherincludes a second number of discrete electrodes, each of the secondnumber of discrete electrodes associated with one of the number of thinelements of the number of EO substrate layers; where the active elementsinclude each of the number of thin elements and each of the number ofthick elements having an associated discrete electrode; where each ofthe number of thin elements includes an equal thickness; and/or whereeach of the number of thick elements includes an equal thickness. Anexample system includes a number of the EO substrate layers, where eachof the number of thin elements includes a thickness of x wavelengthscorresponding to a target electro-magnetic (EM) frequency, where each ofthe number of thick elements includes a thickness of y wavelengthscorresponding to the target EM frequency, where each of x and y compriseinteger values, and where the y value for each of the number of thickelements is at least one greater than the x value for an adjacent one ofthe number of thin elements. In certain embodiments, the x value is one(1), and/or the y value is two (2). In certain embodiments, a first oneof the number of thick elements includes a y value that is smaller thanan x value for a first one of the number of thin elements, for examplewhere the first one of the number of thick elements is not adjacent tothe first one of the number of thin elements. In certain embodiments,the first one of the number of thick elements is in a different one ofthe number of EO substrate layers as the first one of the number of thinelements.

An example system includes an EO substrate layer including an EO activematerial, and further including a number of active elements. The examplesystem includes adjacent ones of the number of active elements having athickness value varying by at least one wavelength corresponding to atarget electro-magnetic (EM) frequency. The example system furtherincludes a high-side electrode layer including a number of discreteelectrodes, each of the number of discrete electrodes associated withone of the number of active elements and positioned on a first side ofthe EO substrate layer; a low-side electrode layer positioned on asecond side of the EO substrate layer; and an insulator layeroperationally coupled to the EO substrate layer, and at least partiallypositioned between geometric gaps of the number of active elements.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes where the number of discrete electrodes areresistive electrodes; a number of the EO substrate layers, and where twoadjacent ones of the number of the EO substrate layers share a low-sideelectrode layer; where a terminating one of the number of EO substratelayers is associated with a reflective low-side electrode layer; and/orwhere the number of EO substrate layers are arranged such that aperpendicular line through the number of the EO substrate layers passesthrough a configured thickness of the active elements of the number ofthe EO substrate layers, the configured thickness including a thicknessselected to apply a progressive phase shift to an incident EM beam.

An example system includes a first EO layer including an EO activematerial, and further including: a first number of active elements; asecond EO layer including the EO active material, and further includinga second number of active elements; a first high-side electrode layerincluding a first number of discrete electrodes, each of the firstnumber of discrete electrodes associated with one of the first number ofactive elements and positioned on a first side of the first EO layer; asecond high-side electrode layer including a second number of discreteelectrodes, each of the second number of discrete electrodes associatedwith one of the second number of active elements and positioned on afirst side of the second EO layer; and a low-side electrode arrangementincluding an arrangement such as: a first low-side electrode layerpositioned on a second side of the first EO layer and a second low-sideelectrode layer positioned on a second side of the second EO layer; alow-side electrode layer positioned on a second side of the first EOlayer and further positioned on a second side of the second EO layer;and a number of low-side electrodes, each positioned on a second side ofthe first EO layer or a second side of the second EO layer, where eachactive element of the first number of active elements and the secondnumber of active elements has an associated one of the number oflow-side electrodes. The example system further includes where the firstEO layer and the second EO layer are arranged such that the first numberof active elements are not aligned with the second number of activeelements.

Certain further aspects of an example system are described following,any one or more of which may be present in certain embodiments. Anexample system further includes: a first number of insulating elements,each of the first number of insulating elements positioned betweenadjacent ones of the first number of active elements; a second number ofinsulating elements, each of the second number of insulating elementspositioned between adjacent ones of the second number of activeelements; and/or an insulator layer operationally coupled to the secondEO layer, and having a number of insulating portions extending at leastpartially between each of the second number of active elements. Anexample system further includes: at least one additional EO layerincluding an additional number of active elements; at least oneadditional high-side electrode layer corresponding to each of the atleast one additional EO layers, each of the at least one additionalhigh-side electrode layers including an additional number of discreteelectrodes, each of the additional number of discrete electrodesassociated with one of the additional number of active elements andpositioned on a first side of the corresponding additional EO layer; andwhere the low-side electrode arrangement further includes one of: anadditional low-side electrode layer or a number of additional low-sidediscrete electrodes; such that each of the additional number of activeelements is operationally coupled to a low-side electrode on a secondside of the corresponding additional EO layer. An example system furtherincludes a number of the additional EO layers; where alternatingadjacent pairs of the EO layers each share one of the low-side electrodelayers; where the first EO layer, the second EO layer, and the at leastone additional EO layer are arranged such that a perpendicular linethrough all of the EO layers passes through an equal thickness of activeelements of all of the EO layers; where the first EO layer, the secondEO layer, and the at least one additional EO layer are arranged suchthat a perpendicular line through all of the EO layers passes through aconfigured thickness of the active elements of all of the EO layers, theconfigured thickness including a thickness selected to apply aprogressive phase shift to an incident electro-magnetic (EM) beam,and/or where a terminating one of the first EO layer, the second EOlayer, or the at least one additional EO layer is associated with areflective low-side electrode layer.

An example procedure includes an operation to receive an incidentelectro-magnetic (EM) beam at a number of active cells of anelectro-optic (EO) material; an operation to apply a voltage to thenumber of active cells, thereby selectively adjusting an opticalcharacteristic of each of the number of active cells; and an operationto reset a voltage between at least two adjacent ones of the number ofactive cells, thereby steering the incident EM beam.

Certain further aspects of an example procedure are described following,any one or more of which may be present in certain embodiments. Anexample procedure includes: resetting the voltage by an amount to applya 2π phase shift between a first one of the number of active cells andan adjacent second one of the number of active cells; resetting thevoltage by an amount to apply a 2πn phase shift between a first one ofthe number of active cells and an adjacent second one of the number ofactive cells, where n includes a small positive integer value; and/orresetting the voltage to a value applying a negative phase shift. Anexample procedure further includes: applying the voltage to the numberof active cells to apply a progressive phase shift to the incident EMbeam; applying the progressive phase shift by applying progressivevoltages to adjacent ones of the number of active cells, and resettingthe progressive voltages at selected intervals of the number of activecells; where the selected intervals of the number of active cellscomprise at least six (6) of the number of active cells in each of theselected intervals; applying a uniform voltage to each of the number ofactive cells, and further applying a distinct uniform voltage toadjacent ones of the number of active cells; applying a voltage gradientto each of the number of active cells; and/or applying a distinctvoltage gradient to adjacent ones of the number of active cells. Anexample procedure further includes: insulating a first high sideelectrode corresponding to a first one of the number of active cellsfrom a second high side electrode corresponding to a second one of thenumber of active cells, where the first one of the number of activecells is adjacent to the second one of the number of active cells;and/or enhancing the insulating in response to the first one of thenumber of active cells and the second one of the active cells includingthe at least two of the number of active cells corresponding to theresetting the voltage. An example procedure further includes steeringthe incident EM beam in a first axis, thereby providing a first axissteered EM beam, and further performing the operations of: receiving thesteered EM beam at a second number of active cells of the EO material;applying a voltage to the second number of active cells, therebyselectively adjusting an optical characteristic of each of the secondnumber of active cells; and/or resetting a voltage between at least twoadjacent ones of the second number of active cells, thereby steering theincident EM beam in a second axis distinct from the first axis. It canbe seen that the operations of the example procedure provide a two-axissteered EM beam.

An example apparatus includes an incident beam circuit that interpretsan EM beam value; a steering request circuit that interprets a steeringprofile value; a steering configuration circuit that determines a numberof voltage values in response to the steering profile value, the numberof voltage values corresponding to a number of active cells of an EOmaterial, the number of voltage values including at least oneprogressive voltage value and a voltage reset value; and a steeringimplementation circuit that provides an EO command value in response tothe number of voltage values.

Certain further aspects of an example apparatus are described following,any one or more of which may be present in certain embodiments. Anexample apparatus includes: where the voltage reset value includes avoltage adjustment between two adjacent ones of the number of activecells to apply a 2πn phase shift between a first one of the adjacentones of the active cells and an second one of the adjacent ones of theof active cells, where n includes a small positive integer value; wherethe steering profile value includes a target location for an EM beam;where the steering profile value includes a target steering angle for anEM beam; where the steering profile value includes a first targetsteering angle for a first steering axis for an EM beam and a secondtarget steering angle for a second steering axis for the EM beam; and/orwhere the EM beam value includes at least one EM beam value selectedfrom the values consisting of: a wavelength value of an incident EMbeam, a presence of an incident EM beam, and a characteristic of anincident EM beam. An example apparatus includes the steeringconfiguration circuit further determining the number of voltage valuesfor a number of layers of active cells of the EO material.

An example procedure includes an operation to interpret anelectro-magnetic (EM) beam value, an operation to interpret a steeringprofile value, and an operation to determine a number of voltage valuesin response to the steering profile value. The number of voltage valuescorrespond to a number of active cells of an EO material, and the numberof voltage values include at least one progressive voltage value and avoltage reset value. The example procedure further includes an operationto provide an EO command value in response to the number of voltagevalues.

Certain further aspects of an example procedure are described following,any one or more of which may be present in certain embodiments. Anexample procedure further includes: where the voltage reset valueincludes a voltage adjustment between two adjacent ones of the number ofactive cells to apply a 2πn phase shift between a first one of theadjacent ones of the active cells and an second one of the adjacent onesof the of active cells, where n includes a small positive integer value;where the steering profile value includes a target location for an EMbeam and/or a target steering angle for the EM beam; where the steeringprofile value includes a first target steering angle for a firststeering axis for an EM beam and a second target steering angle for asecond steering axis for the EM beam; where the steering profile valueincludes a first target steering angle for a first polarity of the EMbeam and a second target steering angle for a second polarity of the EMbeam; and/or where the EM beam value includes at least one EM beam valuesuch as: a wavelength value of an incident EM beam, a presence of anincident EM beam, and a characteristic of an incident EM beam. Anexample procedure further includes an operation to determine the numberof voltage values for a number of layers of active cells of the EOmaterial.

An example procedure includes an operation to provide an EO layerincluding an EO active material, and an operation to form a number ofactive cells of the EO layer, where the forming includes: operationallycoupling a high-side electrode layer including a number of discreteelectrodes to a first side of the EO layer; and operationally coupling alow-side electrode layer to a second side of the EO layer. The exampleprocedure further includes operationally coupling an insulator to thenumber of active cells of the EO layer, where the insulator is at leastpartially positioned between a first one of the active cells and asecond one of the active cells.

Certain further aspects of an example procedure are described following,any one or more of which may be present in certain embodiments. Anexample procedure further includes: providing the EO layer in a castleconfiguration; providing a number of EO layers in a chess configuration;operationally coupling the high-side electrode layer by providing thenumber of discrete electrodes as resistive electrodes; operationallycoupling the high-side electrode layer by providing the number ofdiscrete electrodes as tilted electrodes; and/or operationally couplingthe high-side electrode layer by providing the number of discreteelectrodes as electrodes having a selected geometric arrangement. Anexample procedure further includes: providing the EO layer by providinga number of EO layers, and further forming the number of active cells ofthe EO layer by operationally coupling each one of a number of high-sideelectrode layers to a corresponding one of the number of EO layers;further forming the number of active cells of the EO layer byoperationally coupling a low-side electrode layer such that the low-sideelectrode layer is shared by adjacent ones of the number of EO layers;where providing the EO layer includes utilizing a contiguous substrateof the EO material for the EO layer; where operationally coupling theinsulator includes utilizing a contiguous substrate of insulatormaterial for the insulator; where operationally coupling the low-sideelectrode layer includes utilizing a reflective low-side electrodelayer; where operationally coupling the high-side electrode layerincludes providing the number of discrete electrodes as resistiveelectrodes having a selectable resistance profile; and/or whereproviding the number of discrete electrodes as resistive electrodeshaving a selectable resistance profile includes providing the number ofdiscrete electrodes as solid state electrodes.

An example system includes a high-side electrode layer having a numberof discrete electrodes, a low-side electrode layer, and an EO layerincluding an EO active material at least partially positioned betweenthe high-side electrode layer and the low-side electrode layer, therebyforming a number of active cells of the EO layer. The example systemfurther includes a controller including a steering request circuit, asteering configuration circuit, and a steering implementation circuit.The steering request circuit interprets a steering request value, andthe steering configuration circuit determines a number of EO commandvalues in response to the steering request value, where the number of EOcommand values correspond to a half-wave voltage profile. The steeringimplementation circuit provides a number of voltage commands in responseto the number of EO command values.

Certain further aspects of the example system are described following,any one or more of which may be present in certain embodiments. Anexample system includes the half-wave voltage profile having a firstvoltage value for a last electrode of a first phase delay progression, asecond voltage value for a first electrode of a second phase delayprogression, and where the first voltage value and the second voltagevalue have an equal magnitude and an opposite sign. An example systemincludes each of the discrete electrodes having a length that is aboutequal to a thickness of the EO active layer. An example system includeseach of the discrete electrodes being resistive electrodes.

An example improved modulo 2πn electro-optical or photonic beam steeringscanner includes at least one active EO layer having a first side and anopposing second side, at least one conductive or resistive discreteelectrode, arranged along the first side, at least one ground electrodearranged along the second side, and at least one insulator arranged toextend at least partially into the at least one active EO layer. Theexample improved beam steering scanner further includes where the atleast one conductive or resistive discrete electrode is constructed toimpose one, or more, voltages to change an index of refractionsufficient to cause an OPD change to a beam of light traveling throughthe at least one active EO layer.

Certain further aspects of an improved beam steering scanner aredescribed following, any one or more of which may be present in certainembodiments. An example improved beam steering scanner includes: wherethe at least one active EO layer includes a material such as: EOcrystals, a crystal layer, multiple crystal layers, an EO crystal layer,multiple EO crystal layers, liquid crystals, polymers, crystals with alinear change in index of refraction with respect to an applied electricfield, and/or crystals with a quadratic change in index of refractionwith respect to an applied electric field; where the at least oneconductive or resistive discrete electrode includes at least twodiscrete electrodes and where the at least one insulator is locatedbetween the at least two discrete electrodes to reduce the spread of anelectric field between the at least two discrete electrodes; where theat least one active EO layer includes a material capable of having achange in index of refraction when an electric current is applied to thematerial; where the at least one ground electrode includes a series ofground electrodes and where at least one of the ground electrodes in theseries of ground electrodes is set at a non-zero value; where areflective layer is arranged along the at least one ground electrode,the at least one ground electrode arranged between the at least oneactive EO layer and the reflective layer; where the at least oneconductive or resistive discrete electrode includes at least one tilteddiscrete electrode; and/or where the at least one conductive orresistive electrode includes a set of discrete, transparent electrodes.

Another example improved modulo 2πn electro-optical or photonic beamsteering scanner includes at least two active rows arranged between twosubstrates, the substrates transparent to an incoming optical orphotonic wave, where each active row includes a first side and anopposing second side, and where each active row includes at least twoactive cells separated by at least one insulator cell; at least onediscrete conductive or resistive electrode arranged along the first sideof each active row; and at least one ground electrode arranged along thesecond side of each active row. The example improved beam steeringscanner further includes where an arrangement of the at least two activecells and insulator cells in one of the at least two active rows isopposite to the arrangement of the at least two active cells andinsulator cells in the other of the at least two active rows.

Certain further aspects of an improved beam steering scanner aredescribed following, any one or more of which may be present in certainembodiments. An example improved beam steering scanner includes whereone of the at least one ground electrodes is a last ground electrodethat is either reflective or transparent to an incoming optical orphotonic wave, where the incoming optical or photonic wave is to bedeflected by the scanner; where one of the at least two active cells inone of the at least two active rows is the same size as the at least oneinsulator cell in another of the at least two active rows; where the atleast one ground electrode is a continuous ground electrode; where theat least two active cells include an optically active material, theoptically active material having a refractive index that is changeableby applying a voltage to the at least one discrete electrode; where awavelength of the incoming optical or photonic wave ranges between 0.25and 12 microns; where the at least one insulator cell includes atransparent material with a refractive index close to the refractiveindex of the substrate; and/or where the at least two active rowsinclude four active rows.

An example improved scanner for steering an optical beam includes atleast two active rows arranged between two substrates, the substratestransparent to an incoming optical or photonic wave, each active rowhaving a first side and an opposing second side, each active rowincluding at least two active cells separated by at least one insulatorcell; at least one ground electrode arranged between two of the at leasttwo active rows; and where each of the at least two active rows includesat least one discrete electrode arranged along the first side or secondside of each active row opposite the at least one ground electrode. Theexample improved scanner for steering an optical beam includes where anarrangement of the at least two active cells and insulator cells in oneof the at least two active rows is opposite to the arrangement of the atleast two active cells and insulator cells in the other of the at leasttwo active rows.

Certain further aspects of an example improved scanner for steering anoptical beam are described following, any one or more of which may bepresent in certain embodiments. An example improved scanner for steeringan optical beam includes where the at least one discrete electrode iseither conductive or resistive; where a reflective layer is arranged ona surface of one of the substrates; where the at least one groundelectrode includes a transparent continuous ground electrode; where oneof the at least two active cells in one of the at least two active rowsis the same size as the at least one insulator cell in another of the atleast two active rows; where the at least two active cells includes anoptically active material, the optically active material having arefractive index that is changeable by applying a voltage to the atleast one discrete electrode; where a wavelength of the incoming opticalor photonic wave ranges between about 0.25 and about 12 microns; wherethe at least one insulator cell comprises a transparent material with arefractive index close to the refractive index of the substrate; wherethe at least two active rows includes four active rows; where theoptically active material includes a material such as EO crystals,liquid crystals, and/or quantum dot materials; and/or where the EOcrystals include a material such as PMN-PT, KTN, SBN, PBN, PZT, and/orBaTiO₃.

Referencing FIG. 26, an example beam steering device is depicted. Theexample beam steering device includes a hardware layer 2602 having beamsteering components, including a high-side electrode layer 2606, alow-side electrode layer 2610, and a number of active cells 2608. Theactive cells 2608 are positioned between the high-side electrode layer2606 and the low-side electrode layer 2610, and include an EO activematerial that changes an optical characteristic in response to anapplied voltage or electric field. The example beam steering device mayinclude the EO active material that makes up the substrate of the activecells 2608 provided as discrete elements of the EO active material, oras a monolithic substrate, where portions of the monolithic substrateinterposed between each discrete electrode of a number of discreteelectrodes of the high-side electrode layer 2610 each form one of theactive cells. In certain embodiments, segments of the EO active materialmay form several active cells 2608, with the EO active material formedin more than one segment to create the active cell layer.

The example beam steering device further includes a voltage controller2612 responsive to voltage commands, steering commands, or other similarcommand structures, where the voltage controller 2612 provides voltagecontrol of elements of the high-side electrode layer 2606 and/or thelow-side electrode layer 2610, thereby controlling the voltagedifferential and/or electric field across the active cells 2608. Incertain embodiments, voltage control of the electrode layers 2606, 2610includes raising the voltage of the high-side electrode layer 2606and/or individual discrete electrodes of the high-side electrode layer2610, and may further include lowering the voltage (and/or connecting toa ground) of the low-side electrode layer 2610 and/or individualdiscrete electrodes of the low-side electrode layer 2610. In certainembodiments, the hardware layer 2602 of the example beam steering devicemay include any features and/or elements of any beam steering devicethroughout the present disclosure, including without limitation:insulators interposed (at least partially) between one or more of theactive cells 2608; electrodes provided as discrete or continuouselectrode layers (e.g., where at least one of the high-side electrodelayer 2606 or the low-side electrode layer 2610 is provided as discreteelectrodes, and/or where each of the active cells 2608 is provided witha discrete electrode at the high-side or low-side to provide forindividual voltage differential control for that active cell); tiltedand/or geometrically profiled electrodes; the active cells provided in acastle arrangement, a chess arrangement, or combinations of these; areflective layer or reflective element (e.g., a substrate or groundelectrode provided as a reflective layer, and/or a reflective layerassociated with one of these); and/or an anti-reflective coatingprovided on at least a portion of a layer interface in the hardwarelayer 2602. In certain embodiments, the hardware layer 2602 includesmultiple layers of active cells structured to cooperate to provide oneor more of: steering for more than one polarity; more than one axis;more than one target wavelength of an incident EM beam 2604; additionalsteering capability; and/or to cooperate among distinct hardware layersof active cells for steering a particular wavelength, polarity, and/oraxis.

In certain embodiments, the discrete electrodes 2606 are sized such thata length of an individual discrete electrode 2606 (e.g., the left-rightdistance of the discrete electrode 2606) is the same as, or similar to,a thickness of the active cells 2608. In certain embodiments, the ratioof the length of individual discrete electrodes 2606 to the thickness ofthe active cells 2608 is referenced as the aspect ratio. It has beenfound that having a discrete electrode 2606 that is the same as thethickness of the active cell 2608 (e.g., providing an aspect ratio ofabout 1) minimizes (but does not eliminate) fringing fields betweenelectrodes 2606. In certain embodiments, and without limitation, alength of the discrete electrode 2606 that is the same as, or similarto, the thickness of the active cells 2608 (e.g., having an aspect ratioof about 1) includes: the length and thickness being nominally the same(e.g., allowing for variances and tolerances from manufacturing andassembly processes, and part-to-part variation); a length and thicknessbeing selected such that fringing fields are within a selected amount(e.g., a ratio, an offset value, below a maximum threshold, etc.) of aminimum fringing field value; a closest match between the length andthickness available from nominally available parts (e.g.: off-the-shelfor commercially available electrodes and/or EO materials; a closestmatch from available electrodes and/or EO materials from other systemsalready in production; and/or a closest match of electrodes and/or EOmaterials selected from a range of materials designed for otherconsiderations (e.g.: the sizing of the beam steering device; the numberof progressive phase delay stages and the number of phase delay steps ineach stage; the mechanical integrity of the beam steering device; and/orthe heat transfer environment and/or heat rejection environment of thebeam steering device). In certain embodiments, certain electrodes 2606may have a same or similar length as the thickness of the active cells,and other electrodes 2606 may not have a same or similar length as thethickness of the active cells. For example, electrodes 2606 positionedat a reset position (e.g., the last electrode of a first stage, and/orthe first electrode of a second stage) may be sized to be in closercorrelation to the same length as the thickness of the active cellsrelative to other electrodes 2606 in the same beam steering device. Inanother example, certain electrodes 2606 may be separated by insulators(and/or more capable insulators), while other electrodes 2606 are notseparated by insulators (and/or less capable insulators), withun-insulated electrode 2606 separations having an aspect ratio closer to1, and insulated electrode 2606 separations having an aspect ratiofurther from 1. It can be seen that the electrode 2606 length and/oractive cell thickness 2608 can be tuned to provide a desired fringingfield profile across the beam steering device, for example to utilizefringing fields to smooth the phase profile (e.g., reference FIG. 8)while minimizing fringing field losses, such as at high loss regionslike the reset position.

It can be seen, in view of the various embodiments of the presentdisclosure, that in certain embodiments, electrode 2606 lengths such asλ, ½λ, and/or ¼λ, as well as integer multiples of these, may bedesirable to match the varying thicknesses of active cells 2608, eitherwithin a beam steering device, within a beam steering device layer(e.g., where different layers are provided to steer distinctwavelengths), or between different devices. For example, in a beamsteering device where steering efficiency is a paramount concern, aclose match of electrode 2606 lengths to active cell 2608 thicknessesmay be provided, and in a beam steering device where a smooth phasedelay profile is desired, the match of the electrode 2606 length toactive cell 2608 thickness may be relaxed—even where the beam steeringdevices otherwise are configured to steer a same wavelength of anincident EM beam to a same steering direction capability.

The example beam steering device further includes a steering controller2616 that provides steering commands to the hardware layer 2602. Thevoltage controller 2612 is responsive to the steering commands toprovide the voltage control of elements of the electrode layers 2606,2610, thereby directing the incident EM beam 2604 to the desiredlocation as a steered EM beam 2614. In certain embodiments, the steeringcontroller 2616 and/or the voltage controller 2612 include any aspects,and/or are configured to perform any operations, as referencedthroughout the present disclosure to perform beam steering operations.Without limitation to any other aspects of the present disclosure, thesteering controller 2616 and/or the voltage controller 2612 may includeany aspects or perform any operations of a controller 1902, and/or mayperform any operations as recited in the disclosure referencing FIGS.21-25, and/or any operations recited in the disclosure reference FIG.31.

Referencing FIG. 27, an example beam steering device includes thehigh-side electrode layer 2606, the low-side electrode layer 2610, andthe active cells 2608. In the example of FIG. 27, the high-sideelectrode layer 2606 is provided as a number of discrete electrodes, thelow-side electrode layer 2610 is provided as a common ground electrode,and the active cells 2608 include portions of a monolithic EO activesubstrate layer that are positioned between each of the discretehigh-side electrodes and a corresponding portion of the common low-sideelectrode. In the example of FIG. 27, the beam steering device does notinclude insulators between active cells and/or discrete high-sideelectrodes, but in certain embodiments the beam steering device of FIG.27 is configured to manage fringing field losses to steering efficiencyusing a steering controller 2616 and/or voltage controller 2612 that areconfigured to reduce fringing field losses. In certain embodiments, thebeam steering device of FIG. 27 is implemented with a half-wave voltageprofile, for example as described in the disclosure referencing FIGS.29-31. In certain embodiments, one or more portions of the example beamsteering device in FIG. 27 are provided with an aspect ratio that is 1or about 1.

Referencing FIG. 28, an example beam steering device is depicted,similar to the beam steering device depicted in FIG. 27. The beamsteering device in the example of FIG. 28 includes a discrete high-sideelectrode 2801 and an opposing discrete low-side electrode 2803. Thebeam steering device includes an EO active layer forming active cells2608, with each active cell 2608 formed from a portion of the EO activelayer between opposing electrodes 2801, 2803. In certain embodiments,one or more electrodes may omit an insulator therebetween, and/or thebeam steering device of FIG. 28 may be operated in a half-wave voltageprofile. In certain embodiments, for example depending upon the hardwareand electrode types to implement the desired voltage profile on theelectrodes, the utilization of discrete low-side electrodes 2803 mayprovide for a more convenient development of the voltage profile, suchas by manipulating separate voltages on the low-side electrodes 2803.

In certain embodiments, for example where providing an aspect ratio of 1or about 1 drives the design to a reduced number of electrodes per reset(e.g., due to the size of the aperture and/or beam steering device), ahalf-wave voltage profile may be combined with resistive electrodes,providing for some reduction in quantization losses while achieving thehalf-wave voltage profile advantage for fringing field losses. As willbe described in the disclosure referencing FIG. 30, a half-wave voltageprofile enforces a maximum fringing field region (flyback distance) thatis equal to the distance between discrete electrodes. For comparison, acastle arrangement enforces a maximum flyback distance that is a widthof one discrete electrode, and a chess arrangement enforces a maximumflyback distance that is a theoretical value of zero (e.g., where eachelectrode is surrounded by an insulator, limiting the edge effect at theextent of the electrode). Certain further considerations include thedesirability of an aspect ratio of about 1 for half-wave voltageportions of a beam steering device, the desirability of a match inoptical properties between the substrate and the EO active material fora castle arrangement portion of the beam steering device, and thedesirability of a match in optical properties between the insulator andthe EO active material for a chess arrangement portion of the beamsteering device. One of skill in the art, having the benefit of thedisclosures herein, can readily determine arrangements for a beamsteering device utilizing various features described herein, including:the usage of insulators; a chess arrangement; a castle arrangement;selected aspect ratios; a selected voltage progression including ahalf-wave voltage profile; selected optical properties for the EO activelayer, the substrate, and/or the insulator(s); and/or the utilization ofa reflective layer. Certain considerations in determining which featuresare utilized for a particular beam steering device include, withoutlimitation to any other aspect of the present disclosure: the desireddevice steering capability; steering efficiency; voltages provided andthe control thereof; manufacturing considerations; and/or the desiredsize of the beam steering device.

Referencing FIG. 29, an example steering controller 2616 and voltagecontroller 2612 are configured to reduce fringing field losses in a beamsteering device, including a beam steering device with or withoutinsulating elements. The example steering controller 2616 includes asteering request circuit 2006 that determines steering value(s) 2012,for example steering directions, target locations, steering efficiencyvalues, or the like. In certain embodiments, the steering value(s) 2012include selected wavelengths or frequencies of incident EM radiation,selected polarities, selected steering axes, or other parameters. Theexample steering controller 2616 further includes a steeringconfiguration circuit 1908 that determines EO command value(s) 1910,which may include desired optical characteristics (e.g., OPD changes)throughout the beam steering device that are responsive to the steeringrequest value(s) 2012. In certain embodiments, the EO command value(s)1910 are determined for one or more various layers in the beam steeringdevice, for example layers that are responsive to selected wavelengths,polarities, efficiencies, axes of steering, etc. In certain embodiments,the steering configuration circuit 1908 utilizes a half-wave voltageprofile 2908 to determine the EO command value(s) 1910, which may beutilized for one or more EO active layers in the beam steering device,and/or portions of one or more EO active layers. It can be seen that, incertain embodiments, one or more layers of a beam steering device mayutilize a half-wave voltage profile 2908, while other layers of the beamsteering device may be configured to utilize another voltage profile.The example steering controller 2616 further includes a steeringimplementation circuit 1914 that provides commands to the voltagecontroller 2612 responsive to the EO command value(s) 1910. In certainembodiments, the translation between the EO command value(s) 1910 andselected voltages for various active cells throughout the beam steeringdevice may be performed by the steering implementation circuit 1914(e.g., passing voltage commands directly to the voltage controller2612), or by the voltage controller 2612 (e.g., translating EO commandvalue(s) 1910 into voltage value(s) 2010 for electrodes in the beamsteering device). The example voltage controller 2612 provides thevoltage value(s) 2010 to electrodes (high-side electrodes, or bothhigh-side and low-side electrodes), either by operating voltage controlhardware (e.g., solid state switches, PWM devices, relays, or the like)directly, or by providing voltage value(s) 2010 to a hardware layer thatis responsive to the voltage value(s) 2010 thereby energizing theelectrodes in a manner that implements the EO command value(s) 1910 inactive cells of the beam steering device.

FIG. 30 is an example depiction of a realistic phase profile 2808 which,according to modeling and calculations, it is believed to be achievableusing various aspects of the present disclosure, including a steeringcontroller 2616 and voltage controller 2612 such as depicted in FIG. 29,and/or using a procedure such as that depicted in FIG. 31. In theexample of FIG. 30, the OPD progression 2806 is depicted as being aboveand below a nominal voltage 2804, with a positive and negative voltagerelative to the nominal voltage, and may be referenced as a half-wavevoltage profile. Additionally, in the example of FIG. 30, the aspectratio is provided with a value of about 1. In the example of FIG. 30,the reset occurs between a positive voltage electrode and a negativevoltage electrode. It has been found that a voltage profile such as thatdepicted in FIG. 30, combined with an aspect ratio of about 1, providesfor a rapid reset of the voltage with fringing field region limited tothe distance between electrodes even without the utilization ofinsulators, providing a significant decrease in fringing field losses atthe reset. The example of FIG. 30 depicts resistive electrodes, althoughconductive electrodes may also be utilized. Because the maximum voltagein the EO active layer is one-half of the voltage in a nominal voltagephase delay profile (e.g., reset from a 2π delay voltage to a zero delayvoltage), the thickness of the EO active layer using a half-wave voltageprofile can be one-half of the thickness utilized for a nominal voltagephase delay profile. Additionally, the addition of a reflective layer(e.g., a reflective substrate, reflective ground electrode, or adedicated reflective layer) can provide for a thickness of one-fourththe thickness utilized for a nominal voltage phase delay profile.

In certain embodiments, the utilization of an ultra-thin EO active layer(e.g., ¼λ, which may be 500 nm or less for certain steered wavelengths)provides for additional capabilities. For example, the small physicalfootprint and ease of manufacture provides for the ready addition ofextra layers to steer additional wavelengths, incremental steeringcapability, and/or steering of additional polarities and/or axes ofsteering. In another example, the ultra-thin layer provides forincreased energy throughput capability, as the thin layer absorbs alower fraction of energy flow-through as heat, and has a more favorableheat rejection environment (lower capacity, and a shorter heatconduction path) that is amenable to an active or passive cooling system(e.g., a cooling layer in thermal contact with the reflective layer).

In the example of FIG. 30, the high voltage 2802 of the phase delayprogression may be consistent with a π phase delay, and the low voltage2806 may be consistent with a −π phase delay, such that at the resetposition 108 a 2π (or 2πn) reset is applied, but the total voltage inthe system is relative to the nominal voltage 2804. Accordingly, it canbe seen that the greatest magnitude of phase delay (and correspondingvoltage) that is enforced by any active cell in the example of FIG. 30is π (either +/−π), and accordingly a greatest thickness required for anactive cell can be as low as one-half λ, instead of λ, which isgenerally required when a magnitude 2π phase delay is applied within asingle active cell.

The example of FIG. 30 depicts a symmetrical voltage profile (e.g., thehigh voltage value 2802 and the low voltage value 2806 are both the samedistance from the nominal voltage value 2804), although the voltageprofile may not be symmetrical. Additionally, a half-wave voltageprofile may nevertheless be utilized with a greatest magnitude phasedelay that exceeds +/−π, which may be symmetrical.

Referencing FIG. 31, an example procedure 3100 to steer an incident EMbeam using a half-wave voltage profile is schematically depicted. Theprocedure 3100 includes an operation 2102 to receive an incident EMbeam, and an operation 3104 to determine a steering request value forthe incident EM beam. The example procedure 3100 further includes anoperation 3106 to determine a half-wave voltage profile that isresponsive to the steering request value—for example to provide an OPDprofile on an EO active layer of a beam steering device that isresponsive to the steering request value and the incident EM beam. Theexample procedure 3100 further includes an operation 3108 to providevoltage commands in response to the half-wave voltage profile, therebyconfiguring an EO active layer and steering the incident EM beam. Theexample operation 3108 includes providing a voltage progression acrossthe EO active layer, and providing reset positions where the power of alast electrode (or capacitor) of a first delay stage is approximatelyequal and of opposite sign as the power of a first electrode (orcapacitor) of a second delay stage. An example operation 3108 includesproviding voltages such that the last electrode of the first delay stagehas an approximately equal positive voltage compared to a negativevoltage of the first electrode of the second delay stage.

Referencing FIG. 32, an EO bulk crystal 3210 is equipped with twotransparent electrodes 3214, 3212. The transparent electrodes 3214, 3212are located on opposing sides of EO bulk crystal 3210. The beam steeringapparatus shown in FIG. 32 further comprises a first lens 3204 withfocal length of f₁ and a second lens 3206 with focal length of f₂.Second lens 3206 is located at f₁+f₂ from the first lens 3204. The beamsteering device also comprises a voltage supplier 3216.

The refractive index of the EO crystal slab 3210, or any other materialwhose index of refraction can be changed by the application of anelectric field, is changed by varying the applied voltage on thetransparent electrodes 3212, 3214 attached to both sides of the EO bulkcrystal slab 3210. The linearly polarized beam 3202 which incidents onthe EO bulk crystal slab 3210 by a fixed angle exits the EO bulk crystalslab 3210 with a same angle but its position will be altered by changingthe index of the EO bulk crystal slab 3210 as a result of varying theapplied voltage. That position change is converted to a change in angleby the first lens 3204. Because the beam 3202 is converged by the firstlens 3204, a second lens 3206 is utilized to re-collimate the beam 3202.Thus, the combination of the first lens 3204 and second lens 3206essentially form a telescope. Any form of telescope is suitable for thisapplication, not just the form shown in FIG. 32. Optionally, a mirror3208 is located after the second lens 3206. The deflection angleaddressed by this bulk system can be approximately calculated using thefollowing equation 6:

$\begin{matrix}{{\Delta\theta}_{def} = {\frac{\theta\; d}{f\; 1}\left( \frac{\Delta\; n}{n^{2}} \right)}} & {{EQ}.\mspace{14mu} 6}\end{matrix}$

Where θ is the incident angle, d is the EO crystal slab thickness, f1 isfocal length of the first lens and n is the refractive index of the EOslab 3210.

The deflection angle in the slab 3210 method can be increased withouthaving a thicker crystal or increasing the applied voltage, by havingmore slabs in series, and/or making the last surface of the last slabreflective. Having several slabs 3210 in series and making the lastsurface reflective will make the optical beam travel through more EOcrystals and will result in a higher position change, and therefore ahigher deflection angle, without having to apply a higher voltage. Thetwo sides of each slab 3210, except the right side of the last slab, iscovered by uniform transparent electrodes 3212, 3214. The beam isreflected by the reflective layer of the final slab and goes all the waythrough the EO crystal slabs 3210 again to get a larger position change.The larger position change will result in a wider deflection angle. Anoptional final reflector could be added after the slab exit so theexiting light is going the same direction as the entering light, exceptfor the deflection angle.

Referencing FIG. 33, an example system for steering light using Kerreffect based EO crystals is depicted. This is referred to as bulk beamsteering because the beam steering occurs in a bulk material, not a thinmaterial. Moreover, bulk beam steering does not require any voltageresets. The configuration of the beam and bulk crystals should beconfigured such that the steered beam will not impinge on the side ofthe bulk crystal. Additionally, a large crystal may require highvoltages to apply the desired index change in the crystal. Certainembodiments herein utilize an exit face configuration, for example aconcave exit face configuration, that amplifies the steered amount ofthe beam that is achieved within the bulk crystal, to provide forenhanced steering capability while allowing for a smaller steered amountwithin the bulk crystal body.

To create steering using either the linear or the quadraticelectro-optical effects, a high electric field is applied to the bulkcrystal. The example of FIG. 33 utilizes patterned electrodes 3340, 3345that apply a voltage across steering portions of the bulk crystal 3360.Note that the embodiment depicted in FIG. 33 utilizes electrodes in eachdimension of the crystal, providing for steering in two dimensions. EOcrystals often have distinct steering capability in both dimensions,with the steering capability in one dimension being significantly morecapable than the steering capability in the other dimension.Accordingly, one of the dimensions (e.g., electrodes 3340 or 3345) maybe omitted, with the system steering in only one dimension, and/ordiscrete slab portions may be utilized to steer the beam in a seconddimension (e.g., passing from a first slab oriented in a first steeringdirection, and the second slab oriented to steer in the second steeringdirection).

Referencing FIG. 34, rectangular shaped electrodes 3450, 3452 arearranged on the opposite sides of the Kerr effect crystal 3360 from eachpatterned/triangular shaped electrode 3340, 3345, for example asgrounding or low-side voltage electrodes. The rectangular electrode3450, 3452 in the example of FIG. 34 are kept away from the long sideedges of the crystal to prevent arcing. Any arrangement of low-sideelectrodes 3450, 3452 is contemplated herein, and the positioning of theelectrodes and/or proximity of the electrodes to the edges may bedetermined based upon the high-side voltage electrode 3340, 3345configurations, the desired steering in the bulk crystal 3360, and/orthe voltages present in the system during steering operations. Theexample rectangular electrodes 3450, 3452 can be used as a ground plane,but can be kept at any voltage.

As FIGS. 33 and 34 disclose, an embodiment includes at least fourtriangular/patterned electrodes, two top conductive electrodes 3345 andtwo side conductive electrodes 3340. This embodiment also includes atleast four low-side voltage electrodes on opposing sides of the bulkcrystal 3360 relative to the high-side electrodes 3345, 3340. Theexample embodiment includes a top polarizer conductive electrode 3370,arranged between the top conductive electrodes 3345. In the example, thepolarizer conductive electrode 3370 allows for rotating the lightpolarization between steering portions of the bulk crystal 3360.Additionally or alternatively, bulk crystal 3360 portions may be rotatedfor each steering portion (or a subset of steering portions), with ahalf-wave plate, anti-reflective coating, or other configuration tomanage the steered incident beam traversing between steered portionsthat may have different steering orientations. In the example of FIG.34, an additional polarizing electrode 3345 is provided between thelow-side electrodes 3450.

In certain embodiments, the bulk crystal 3360 is operated in the Kerreffect region, and polling of the ferroelectric domains is not required,allowing for electrodes on two sides of the crystal 3360, with steeringin two dimensions within the same section of the crystal 3360. Incertain embodiments, steering may be performed in two dimensions inseparate sections of the crystal 3360, for example to enhance thesteering capabilities in each dimension. In certain embodiments, thebulk crystal 3360 may be operated in a Pockels effect region, thus thebulk crystal 3360 may be operated in either the paraelectric (Kerreffect) or the ferroelectric (Pockels effect) region, depending upon theselected crystal, operating temperature, and desired steering voltagesto be utilized.

While FIGS. 33, 34 depict each steering section of the crystal 3360 asthe same length, each steering section can be any length. The embodimentof FIGS. 33, 34 is for illustrative purposes of one possibleimplementation. In addition. the amount of angular beam steering doesnot have to be the same in each direction.

Referencing FIG. 35, an embodiment comprising a single EO crystal 3500in an appropriate crystal class such as 4 mm or 3 m is depicted, withthe electric field in a single direction, to do beam steering in bothdimensions, rather than using 2 crystals. Additionally or alternatively,both steering portions of the embodiment of FIG. 35 may be applied tothe same steering dimension, allowing for enhanced steering capabilityin the steered dimension. The embodiment further includes EO crystal3500 having a top shaped or patterned electrodes 3510 with a polarizingelectrode 3520 therebetween. In certain embodiments, the crystal 3500may include two bulk crystal portions adjoined and oriented at distinctaxes, with the polarizing electrode 3520 additionally or alternativelyincluding a half-wave plate or anti-reflective coating. Referencing FIG.36, in the embodiment depicted there are additionally included bottomelectrodes 3615 that provide the low-voltage side match for electrodes3510, with a low-side polarizing electrode 3625, half-wave plate, and/oranti-reflective coating optionally provided between steering portions.The electrode pattern shown on the bottom of the EO crystal 3500 in FIG.36 is similar to the electrode pattern on the top shown in FIG. 35,although the low-side electrodes may be in any configuration includingrectangular electrodes, a common ground electrode, etc. A correct fixedDC voltage is applied on polarizer electrode 3520 (where present) butany voltage can be applied to electrodes 3510, 3615. Because theelectric field is applied in one direction, the deflection angle in onedimension will be smaller than the other dimension. That can be slightlycompensated by increasing the length and/or the applied voltage on theelectrodes responsible for steering to that dimension.

A benefit of the FIGS. 35, 36 embodiment is to allow beam steering foreither Kerr effect or Pockels effect crystals while only using a singlecrystal, polled in only a single direction. In certain embodiments,polarization is rotated between sections of the EO crystal 3520. Becauseof the properties of the EO crystal 3500, rotating the polarizationcauses the beam to steer in a different dimension.

Referencing FIG. 37, an example EO crystal 3730 performs beam steeringto a wide angle, in one or both dimensions, within a compact structure.The example of FIG. 36 may utilize a single crystal to perform steeringin both directions, and/or may include two integrated crystal portionseach having a distinct steering axis, with a polarizing electrode 3760,a half-wave plate, and/or an anti-reflective coating interposed betweenthe steering portions (e.g., the crystal portion 3730 influenced byelectrode 3740 as a first steering portion, and the crystal portion 3732influenced by electrode 3745 as a second steering portion, in theexample of FIG. 37). Referencing FIG. 38, an opposing side of theembodiment of FIG. 37 is depicted, with opposing low-side electrodes3850, 3855 and an opposing low-side polarizing electrode 3865 depictedin the example. As described throughout the present disclosure, low-sideelectrodes 3850, 3855 may be shaped to match the high-side electrodes3740, 3745, provided as a lower voltage, negative voltage, and/orground/reference voltage, and/or may be included as common groundelectrodes.

Referencing FIG. 39, an embodiment is depicted that is similar to theembodiment depicted in FIGS. 37 and 38, with additional steeringportions added to enhance the steering capability of the bulk steeringdevice. The embodiment of FIG. 39 depicts sequential steering portionsof a bulk crystal 3930, 3934 (which may be integrated abutting steeringcrystals having distinct orientations) with associated high-sideelectrodes 3945, 3940 in the appropriate steering dimensions. Althoughthe embodiment of FIG. 39 depicts alternating steering dimensions (e.g.,XYXY), in certain embodiments the steering dimensions may be sequencedin any manner (e.g., XXYY, or XYYX). Additionally or alternatively, theexample of FIG. 39 depicts four steering portions (e.g. XYXY), althoughany number of steering portions may be provided within a given steeringdevice. Additionally or alternatively, the number of steering portionsassociated with each steering direction, where more than one steeringdirection is applied, may be the same number or a different number(e.g., XXYYY, XXXXY, XXYXX, etc.). It can be seen that grouping steeringin the same dimension within sequential portions may provide for certainefficiencies (e.g., fewer transitions between crystal interfaces and/orpolarizing portions), while switching steering dimensions betweensequential portions may improve the overall capability for steeringwithout impinging on the side of a given crystal section. To steer tolarger angles, the embodiment shown in FIG. 37-38 (or FIG. 39) can berepeated as desired. Additionally or alternatively, for example asdepicted in other embodiments of the present disclosure, the size of thecrystal 3930 may be increased as the steering portions progress tocompensate for the steering of the incident EM beam. Additionally oralternatively, the size progression of the crystal 3930 can bedimensionally configured—for example a greater increase in an X steeringdirection than in a Y steering direction, for an example where the Xsteering angle is greater than the Y steering angle.

In certain embodiments, as depicted in FIG. 39, the beam is steeredpartially in one direction and then steered at least partially in asecond direction through steering portions of the crystal. Accordingly,the incident EM beam is steered gradually in each direction and thepolarization of light is flipped as needed by the polarizer electrodes3960 (and/or integrated half-wave plates, and/or utilizing re-orientedcrystal portions) to make the light see the index change in differentdirections. The steering to each direction is done incrementally, and insuccessive steps. Similarly, voltages applied at electrodes 3940, 3945for each steering portion are applied selectively to provide the desiredsteering in each steering portion, and appropriate voltages are appliedfor each polarizing electrode 3960 (where used). An example utilizesselected DC or AC voltages for adjusting steering angles, and fixed DCvoltages for rotating the light polarization (where used) to make thelight see the index change in another direction.

Referencing FIG. 40, an opposite side of the steering device depicted inFIG. 39 is depicted. The example steering device of FIG. 40 depictsopposing low-side electrodes 4055, 4050 corresponding to each of thehigh-side electrodes 3945, 3940 of the embodiment of FIG. 39, andcorresponding low-side polarizing electrodes 4065 corresponding to eachof the polarizing electrodes 3960 of FIG. 39. The low-side electrodearrangement of FIGS. 39-40 may be any configuration as describedthroughout the present disclosure, and may include matching geometries,simplified geometries, lower or negative voltages, ground voltages, etc.

Referencing FIGS. 41-42, an example embodiment of a bulk steering devicehaving high steering capability in a selected dimension is depicted. Theexample of FIG. 41 includes sequential bulk EO crystal portions 4175,4170, 4165, 4160 having an increasing size in the steered direction. Theexample of FIG. 41 includes a number of discrete crystal portions havingan increasing size, which may include an integrated crystal manufacturedas shown, and/or adjoined crystal portions (including, in an example, ananti-reflective coating between adjoining portions, such as when anindex between each portion may be distinct). The example of FIG. 41includes discrete crystal portions of increasing size, but the crystalmay additionally or alternatively increase in a continuous fashion(e.g., a flaring shape), and/or in combinations of discrete sizedportions and continuously increasing size portions. The example of FIG.41 includes high-side electrodes 4110, 4115, 4120, 4125 associated witheach steering portion and configured to apply a selected voltage to eachassociated steering portion. Referencing FIG. 42, an opposite side ofthe embodiment of FIG. 41 depicts low-side electrodes 4245, 4240, 4235,4230 associated with each of the steering portions. The low-sideelectrode arrangement of FIG. 42 may be any configuration as describedthroughout the present disclosure, and may include matching geometries,simplified geometries, lower or negative voltages, ground voltages, etc.The embodiment of FIGS. 41-42 allows for significant steering angleswithin the bulk crystal without impingement of the steered incident EMbeam onto a side of any one of the steering portions, while minimizingor reducing the amount of bulk crystal material, applied voltages, andthe like.

As discussed above, EO crystals 4175, 4170, 4165, 4160 may include othermaterials whose index is modified by the application of an electricfield. If W_(i) and L_(i) are the width and length of each of the bulkcrystals (and/or the width and length of each of the steering portions),a preferable number of triangular electrodes may be approximatelydetermined using the following equation 7:

$\begin{matrix}{N_{opt} = {0.87\frac{L_{i}}{W_{i}}}} & {{EQ}.\mspace{14mu} 7}\end{matrix}$

For the embodiment depicted in FIGS. 41-42, the deflection angle of thesteered incident EM beam can be calculated using the following equation8. Equation 8 may be utilized as a design time equation, for example todesign the bulk crystal and/or steering portions having a desiredsteering capability, and/or equation 8 may be utilized as a run-timeequation, for example to determine the indices to be applied at each ofthe steering portions (and therefore the applied voltages at theelectrodes) to achieve a steering request value and/or steering commandvalue (or other selected steering amount).

$\begin{matrix}{\theta_{f} = {\Delta\; n\;\Sigma\frac{L_{i}}{W_{i}}}} & {{EQ}.\mspace{14mu} 8}\end{matrix}$

Referencing FIG. 43, an example bulk steering device includes a bulkcrystal having a first end 4362, for example where an incident EM beamis received, and a second end 4360, for example where a steered incidentEM beam is emitted. The example of FIG. 43 includes a number ofsuccessively sized electrodes 4310, 4315, 4320, 4325 structured toprovide selected indices within the crystal as the incident EM beam issteered. The example of FIG. 43 provides a similar practical steeringcapability to the example of FIGS. 41-42, with a simplified crystalgeometry. It can be seen that the example of FIG. 43 includes portionsof the crystal that are not utilized in the active steering of theincident EM beam, but trades excess unutilized crystal material forsimplification in manufacturing and fabrication of the bulk crystaldevice.

The high-side electrodes 4310, 4315, 4320, 4325 are depicted as having asize and position to implement selected steering portions of the deviceto provide the desired steering capability. However, the high-sideelectrodes may have any configuration, and may be configured duringdesign-time or run-time, for example with pixelated high-side electrodeportions (e.g., solid state devices) that may be controllable to providethe selected voltages, and therefore actuation of high-side electrodeportions in run-time. In the example, with a grid of pixelated electrodeelements positioned on the bulk crystal, the size and spacing ofelectrode elements 4310, 4315, 4320, 4325 may be configured duringrun-time of the crystal to provide for flexible capability. The sizingand spacing of electrodes and steering portions in the example of FIG.43 may be provided in accordance with equations 7 and 8 as set forthpreceding, with the length and width of crystal portions adjusted to beeffective lengths and widths in accordance with the electrodepositioning. The example of FIG. 44 provides an opposite side view ofthe embodiment of FIG. 43, with opposing low-side electrodes 4445, 4440,4435, 4430 positioned on the opposite side 4464 of the bulk crystal. Asin the example of FIG. 43, the low-side electrodes may be pixelated,solid state electrode elements, and/or may be any configuration asdescribed throughout the present disclosure, and may include matchinggeometries, simplified geometries, lower or negative voltages, groundvoltages, etc.

As seen in the embodiments shown in FIGS. 41-44, discrete electrodepatterns to steer the linearly polarized beam to a larger angle are usedcompared to conventional deflectors. In FIGS. 41-44, the deflectionangle is increased by reducing the width of the discrete triangularelectrodes at the input of the crystal and gradually increasing thewidth of the discrete triangular electrodes, potentially up to the widthof the rectangular EO crystal 4360.

Referring to FIGS. 45 and 47, an embodiment of the bulk crystal steeringdevice includes the deflection angle being increased by reducing theelectrode 4580 width at the input of the crystal and graduallyincreasing it to the width up to the width of the rectangular EO crystal4500. Increasing the width of the electrode can be either linear, asshown in FIG. 45 or nonlinear, as shown in FIG. 47 in relation tocrystal 4740. In FIGS. 45 and 47 the top electrode 4580, 4720 isresistive, with a voltage gradient across the electrode. In certainembodiments, the electrode 4580, 4720 is shaped in accordance with thevoltage potential applied across the crystal 4500, 4740 (e.g., linear ora non-linear response), and/or to ensure steering of the incident EMbeam as it traverses through the crystal 4500, 4740. Referencing FIGS.46 and 48, the opposite side of the embodiments of FIGS. 45 and 47,respectively, are shown with a ground electrode 4685, 4825 positionedthereon and in a similar geometry to the electrodes 4580, 4720. As inthe example of FIG. 43, the high-side electrodes 4580, 4720 and/orlow-side electrodes 4685, 4720 may be pixelated, solid state electrodeelements, and/or may be any configuration as described throughout thepresent disclosure, and may include matching geometries, simplifiedgeometries, lower or negative voltages, ground voltages, etc.

In the embodiment shown in FIGS. 45 and 46, the electrode 4580, with itslinearly increasing width, is arranged on a top side of bulk EO crystal4500. Electrode 4580 may comprise a resistor. Bottom electrode 4585,also with a linearly increasing width, is arranged on a bottom side ofbulk EO crystal 4500. Bottom electrode 4685 may also comprise aresistor.

FIG. 47 shows a nonlinear shaped electrode 4720 arranged on a top sideof bulk EO crystal 4740. Nonlinear shaped electrode 4720 may comprise aresistor. A second electrode 4825 is arranged on the bottom side of EOCrystal 4740. If L is the length of the crystal, and W_(i) and W arerespectively the inlet width and crystal width, the angle of deflectionmay be calculated using the following equation 9:

$\begin{matrix}{\theta_{f} = \frac{L\;\Delta\; n}{\overset{\_}{w}}} & {{EQ}.\mspace{14mu} 9}\end{matrix}$

Where the W is logarithmic mean of W_(i) and W. In certain embodiments,equation 9 may be utilized as a design time equation (e.g., designingthe width of the crystal and/or configuration of the electrodes) and/oras a run time equation (e.g., controlling the voltage, and thereforeindex of refraction) to steer the incident EM beam as desired.

Referring now to FIG. 49, instead of using resistor electrodes, as inthe embodiments shown in FIG. 45 and FIG. 47, triangular conductive(e.g., silver) electrodes may be used. Specifically, EO bulk crystal4960 comprises a top 4962 where a series of non-discrete conductiveelectrodes 4980, 4975, 4970 are located. Referencing FIG. 50, a secondseries of non-discrete conductive electrodes 5085, 5090, 5095 arearranged on the bottom 5064 of EO crystal 4960. The first and secondseries of non-discrete conductive electrodes may comprise more or lessthan three electrodes. An example single bulk EO crystal 4960 should bepolled to work in the ferroelectric region. The number of triangularelectrodes for a rectangular EO crystal with length of L and width of Wmay be calculated from the equation 7. An example embodiment of FIG. 21includes a same voltage applied on the triangular electrodes 4980, 4975,4970, although distinct voltages may be applied to achieve the desiredsteering of the incident EM beam.

Referring to FIG. 51, another embodiment for deflecting the beam to alarger angle is depicted. The example of FIG. 51 includes a singlebutterfly deflector having an EO bulk crystal 5100 having a first topconductive electrode 5110 and a second top conductive electrode 5120arranged on a top side of EO bulk crystal 5100. First top conductiveelectrode 5110 and a second top conductive electrode 5120 are triangularin shape and are arranged on the top side such that each of saidelectrodes longest sides run along the outside edges of the top side'slongest sides and the vertex of each triangle points to a centerline5104 of the top side. EO bulk crystal 5100 further comprises a first end5106 and a second end 5108 that are perpendicularly disposed between thetop side and a bottom side of the crystal 5100. The first end 5106comprises a light entering portion 5130 and a first reflective portion5140 separated by the centerline 5104. The second end 5108 comprises alight exit portion 5160 and a second reflective portion 5150. In theexample of FIG. 51, an incident EM beam enters the first end 5106,reflects off the second reflective portion 5150, reflects off the firstreflective portion 5140, and exits the bulk steering device.Accordingly, the incident EM beam traverses the bulk steering devicethree times before exiting.

Referencing FIG. 52, another perspective of the example steering deviceof FIG. 51 is depicted. Referencing FIG. 53, an opposite (bottom, in theexample) side of the example steering device of FIG. 51 is depicted. Theexample of FIG. 53 includes a first bottom conductive electrode 5170 anda second bottom conductive electrode 5180 arranged on the bottom side ofthe bulk steering device, separated by a centerline 5114 on the bottomside. In the example, the first bottom electrode 5170 is arrangedopposite the first electrode 5110, and the second bottom electrode 5180is arranged opposite the second electrode 5120. Consequently, the vertexof the first 5170 and second 5180 bottom electrodes point to thecenterline 5114 of the bottom side. The linear polarized beam enterscrystal 5100 at the light entering portion 5130. The beam will bedeflected by the crystal and hits the reflective portions 5140, 5150 andfinally exits EO bulk crystal 5100 after two times of reflection, thus,traversing the crystal three times. The angle of deflection provided bythe butterfly deflector can be calculated using the following equation10.

$\begin{matrix}{\theta_{f} = \frac{3L\;\Delta\; n}{W}} & {{EQ}.\mspace{14mu} 10}\end{matrix}$

Where L and W are the length and width of the crystal. As shown, theangle of deflection in butterfly deflector will be simply three timesmore than conventional EO beam deflector with the same length, width,and applied voltage.

Referencing FIG. 54, an example varifocal lens (VFL) 5400 consistentwith certain embodiments of the present disclosure is depicted. Theexample varifocal lens includes a bulk EO crystal material 5410,responsive to applied voltage gradients to adapt an index of refractionand/or birefringence therein. In the example of FIG. 54, an appliedvoltage gradient forms an affected area 5410 of the VFL, providing foran increased voltage gradient away from the center of the VFL, and areduced or zero applied voltage at a center of the VFL. The VFL may havea voltage gradient applied in a single dimension, for example withlinear electrode elements provided on each of two sides of the VFL(e.g., reference FIG. 65 and the related description), or in twodimensions (e.g., an embodiment of FIG. 65 with four linear electrodeelements, and/or embodiments such as FIG. 55 and the relateddescription). It can be seen that incident EM beams on the VFL willexperience a differential index effect across the VFL with the voltageapplied, such as incident EM beam 5404 relative to incident EM beam5406, and accordingly the VFL will act as a lens, in either one or twodimensions. A VFL, as utilized herein, includes any embodiments of acontrolled lens effect such as those depicted in FIGS. 54, 55, and/or65, including in one or two dimensions, as applicable to the context ofthe VFL and the related system.

Referencing FIG. 55, an example embodiment includes a pair of VFLs 5400,configured such that an incident EM beam passing through the VFLs 5400will be offset and in a same direction as an incident EM beam. In theexample of FIG. 55, a high-side electrode 5403 is provided as anenclosed shape (a circle, in the example of FIG. 55), where a center5404 of the shape will experience a balanced zero voltage, andaccordingly the example of FIG. 55 depicts a pair of two-dimensionalVFLs 5400. In the example of FIG. 55, and/or in other embodiments setforth herein utilizing a pair of VFLs 5400, a voltage gradient of thefirst VFL 5400 (e.g., the left-side VFL) may be reversed from thevoltage gradient of the second VFL 5400 (e.g., the right-side VFL), forexample providing an equivalent convergence and divergence amounts inthe VFLs 5400, and accordingly providing for an emitted EM beam having asame convergence/divergence profile as an incident EM beam. The voltagegradient reversal, where present, may be provided by any configurationavailable, including at least a reversal of the applied voltage (e.g., anegative or positive voltage), a reversal of electrode positions, and/ora geometric facing change of the appropriate VFL 5400. It can be seenthat for other enclosure shapes than a circle (e.g., an ellipse), theeffective lens shape will be different than that shown in FIG. 54, butcan be determined according to the final voltage gradient (or field)applied across the bulk crystal portion of the VFL. In certainembodiments, utilization of a closed shape other than a circle, and/orutilization of linear electrodes having distinct applied voltages and/orgeometries (e.g., reference FIG. 65) allow for the adjustment of the VFL5400 to apply separate lensing effects in separate dimensions, toaccount for distortions applied by other components of a systemincluding the VFL 5400, etc. In certain embodiments, a VFL 5400 such asthat depicted in FIG. 55 may include a ground electrode, and/or aresistive ground electrode, on an opposite side of the bulk crystalrelative to the high-side electrode 5403. In certain embodiments, theground electrode and/or resistive electrode may be grounded in a centerlocation (or other desired zero voltage location) of the groundelectrode. In certain embodiments, one or more of the high-sideelectrode 5403 and/or the ground electrode may be transparent to anincident EM beam, allowing for the electrode to be within the plannedoptical paths (and/or viewing area) of the VFL 5400 without affectingthe operations of the VFL 5400 or the incident EM beam.

Referencing FIG. 56, an example system including VFLs 5400 is depicted.The example VFLs 5400 include any embodiments consistent with thedescriptions throughout the present disclosure, including at least FIGS.54, 55, 65, and the related descriptions. An incident EM beam 5602interfaces with a first VFL 5400 (the left-side VFL in the example), isconverged and interfaces with the second VFL 5400 (the right-side VFL inthe example), and exits the second VFL 5400 linearly offset, and/orsteered, relative to the incident EM beam 5602. In certain embodiments,the first VFL 5400 may diverge the incident EM beam 5602, and the secondVFL 5400 may converge the incident EM beam 5602. In certain embodiments,for example where another system element applies a convergence ordivergence to the incident EM beam 5602, the VFLs 5400 may work together(and/or an effect of one VFL 5400 may be stronger than an opposingeffect of the other VFL 5400) to net converge or net diverge theincident EM beam 5602. For example, where a concave face of a bulksteering crystal applies a divergent effect to a steered EM beam 5602(e.g., reference FIGS. 59, 64, and the related descriptions), the VFLs5400 may be configured to effectively converge the incident EM beam 5602to offset the divergence element applied by other components in thesystem. The VFLs 5400 are displaced by a distance 5604 to ensure thatthe incident EM beam 5602 successfully engages the second VFL 5400(e.g., the right-side VFL) from the first VFL 5400, and further that thesteered EM beam is properly focused between the VFLs 5400.

In certain embodiments, a VFL 5400 includes an EO crystal slab cutthrough it z-axis and poled parallel to its thickness direction. Anexample high-side electrode is positioned on a first side of the EOcrystal slab, and a transparent ground electrode, which may beresistive, is positioned either within the high-side electrode, or on anopposite second side of the EO crystal slab from the high-sideelectrode. Another example VFL 5400 includes a high-side electrode(e.g., a circular or other closed configuration) provided on each sideof the EO crystal slab, with each high-side electrode having a low-sideelectrode, each of which may be resistive, positioned within eachcorresponding high-side electrode. A voltage is applied on the high-sideelectrode(s), and in an example embodiment the transparent groundelectrode is grounded in a center location (either centered in onedimension or two dimensions), making the refractive index of the EO slabchange in response to the external electric field. The change in therefractive index will be the highest at the slab area close to theboundary of the high-side electrode (e.g., along the outer circle in theexample of FIG. 55) and zero in the center location (and/or at theground location). The OPD associated with this structure will be (n)L,where n is the EO slab index change and L is the slab thickness.Accordingly, the EO slab will respond as a lens to applied voltage atthe high-side electrode. By changing the voltage on the high-sideelectrode, the external electric field will change and therefore theindex changes and the OPD and the focal length of the slab (VFL 5400)will vary.

Referencing FIG. 57, an example steering device includes two VFLs 5400displaced by a distance 5604. In certain embodiments, the steeringdevice of FIG. 57 can steer a large aperture beam continuously and witha lower voltage than previously known systems, as large crystal bulkstructures are not required that would lead to large voltagedifferentials across components of the system. High voltage componentsmay be costly, require a large and/or heavy power supply, and/or mayinduce other design limitations (e.g., to limit arc events within thesteering device). The voltages for VFLs, as recited herein, areindependent of the supported aperture size, and/or have a small increasefunction with aperture size to achieve the voltage required to impose atransverse electric field on the steering bulk crystals of the VFLs, asthe required voltages for the VFLs 5400 vary with the thickness of thebulk crystal and not with an area or a linear dimension associated withthe area. The beam size of the incident EM beam 5602 may be affectedslightly after steering with the device of FIG. 57, but wall impingementwithin a steering structure is unlikely, as the VFLs 5400 apply onlyconvergence or divergence to the incident EM beam 5602, and do not applydeflection within the bulk crystal structures of the VFLs 5400. Incertain embodiments, the steering device of FIG. 57 further includesextension lenses 5702, which may be either conventional lenses orfurther VFLs 5400, to ensure that the incident EM beam 5602 successfullytraverses between the steering VFLs 5400. The lenses 5702 may further beutilized to reduce or eliminate optical aberrations in the steered EMbeam. In certain embodiments, the VFL 5400 focal lengths are compensatedto keep the focal planes of the VFLs 5400 in coincidence.

In an example of FIG. 58, each VFL 5400 includes an EO bulk crystalwhich is equipped with two round electrodes (one on each side) and twocircular transparent resistors (or low-side electrodes, each within anassociated round electrode). The round electrodes are located onopposing sides of EO bulk crystal and the transparent resistors arelocated inside the round electrodes. The beam steering apparatus shownin FIG. 28 further includes conventional lenses 5702 to vanish theprobable optical aberration. The VFLs 5400 are displaced by somedistance, but their focal planes are kept coincided at all times duringsteering operations. The VFLs 5400 can be both converging or onediverging and one converging. More than two VFLs 5400 and/or more thantwo conventional lenses 5702 can be used in the scanner. The beamsteering device also includes voltage controllers/supplies 5805, whichapply the desired voltage gradients across the VFLs 5400.

The refractive index of the EO crystal slab, or any other materialswhose index of refraction can be changed by the application of anelectric field, is changed by varying the applied voltage on the roundelectrodes attached to each side of the EO bulk crystal slab. Thelinearly polarized incident EM beam 5602, which incidents on the firstEO bulk crystal slab gets converged or diverged, and then getscollimated and deflected by the second EO bulk crystal slab, because thefocal planes of the first and second slabs always coincide, and thebecause the second slab is vertically (e.g., in a steering relevantdirection) displaced with respect to the first slab. An exampleembodiment includes adjusting the applied voltage on the round electrodeof the first slab being compensated with an adjustment to the voltageapplied on the round electrode of the second slab to make the focalplanes of those slabs always meet. Thus, the combination of the firstand second slabs essentially form a displaced telescope. Any form oftelescope is suitable for this application, not just the form shown inFIG. 58. Optionally, some actual optical surfaces like diverging orconverging lenses can be employed between the slabs (e.g., asconventional lenses) to vanish any probable optical aberrations andensure proper progression of the incident EM beam 5602 between the VFLs5400. More than two EO slabs can be used and the VFLs 5400 can be bothconverging or one can be converging and the other can be diverging, orany other combinations of more than two slabs to make a displacedVFL-based telescope.

Referencing FIG. 59, an example steering device is provided that allowssteering to larger angles in one dimension or two dimensions. Theexample device includes a concave face 5902, wherein an incident EM beamis received at a first end of the beam steering device (e.g., the rightside in the example of FIG. 59), and emitted at the concave face 5902after being steered through one or more steering portions (e.g., as inFIG. 37. The concave face 5902 may be any shape or configuration, suchas conical, parabolic, or the like. The exiting EM beam is furthersteered on emission through the conical face 5902, effectivelyamplifying the steering that is performed within the bulk crystal of thesteering device before emission. The example steering device may includeas many steering portions as desired before the concave face 5902. Incertain embodiments, the concave face 5902 may be concave in a singledimension (e.g., reference FIG. 64 and the related description), or intwo dimensions (e.g., as depicted in FIG. 59). The concave face 5902 maybe symmetric, for example as a conical cap and/or a spherical cap. Theconcavity of the concave face 5902 may be varied in each dimension, forexample as an ellipsoid cap, a hyperboloid cap, and/or an ellipticparaboloid cap. In certain embodiments, the additional steering providedat the concave face 5902 is compensated within the steering portions ofthe bulk crystal, for example with a schedule of steering commands (andcorresponding voltage commands to electrodes) to provide for theincident EM beam to intersect the concave face 5902 at a selectedlocation, thereby resulting in a selected final steering value onemission through the concave face 5902. In certain embodiments, the beamsteering device includes a flared portion 5970 which may be provided,for example, to ensure that the steered EM beam does not impinge on anouter wall of the bulk crystal during steering operations. In theexample of FIG. 59, the flared portion 5970 is depicted near the end ofthe beam steering device, but the entire bulk crystal may be flared orhave size adjustments (e.g., reference FIGS. 41 and 64, and the relateddescriptions) as described throughout the present disclosure to ensurethe desired trajectory of the steered EM beam.

Another embodiment for steering an incident EM beam in to two dimensionsis shown in FIG. 60. The example of FIG. 60 includes patterned high-sidevoltage electrodes on two sides (e.g., electrodes 6010 and 6020) of thebulk crystal, with opposing low-side voltage electrodes on opposingsides of the bulk crystal (not shown). The example patterned high-sideelectrodes 6010, 6020 are a series of triangular electrodes, withheights that are shorter near the inlet face (e.g., the right side ofFIG. 60) and gradually become longer through the length of the crystal.The example of FIG. 60 includes two-dimensional steering of an incidentEM beam, with some overlap between X-steering and Y-steering portions,rather than discrete steering portions, each in only one of the steeringdimensions. Referencing FIG. 61, an example beam steering devicecombines the concave face 5902 with the overlapping dimensional steeringof the embodiment of FIG. 60. The embodiment of FIG. 61 includes firsthigh-side voltage electrodes 6102 to steer in a first direction, andsecond high-side voltage electrodes 6104 to steer in the seconddirection. In the example of FIG. 61, as with other examples utilizing aconcave face 5902, the curvature and/or slope of concavity in eachdirection may be different, for example to compensate for differentialsteering capability in each dimension within the bulk crystal of thebeam steering device.

Referencing FIG. 62, an example beam steering device is depictedincluding a thin beam steering device 6206. The example thin beamsteering device 6206 may be any modulo 2π phase shifting device,including a number of active cells with voltage resets, as describedthroughout the present disclosure, for example in FIGS. 5-31 and therelated descriptions. In certain embodiments, the thin beam steeringdevice 6206 may be in a castle configuration, a castle proconfiguration, a chess configuration, or a chess pro configuration. Incertain embodiments, the thin beam steering device 6206 may include oneor more layers of thin beam steering devices. The example of FIG. 62additionally includes a convex lens portion 6202 and a concave lensportion 6204. In certain embodiments, an incident EM beam enters thebeam steering device at the convex lens portion 6204, traverses throughthe thin beam steering device 6206, and is emitted from the surface ofthe concave lens portion 6206. In certain embodiments, the embodiment ofFIG. 62 is referenced as a zero-power meniscus lens embodiment, as thelens portions 6202, 6204 are operative with an unpowered lens. Theconvex lens portion 6202 converges the steered EM beam, and the concavelens portion 6204 amplifies the steering of the EM beam, while divergingthe steered EM beam (offset by the convergence of the convex portion).While the embodiment of FIG. 62 may utilize an unpowered lens, incertain embodiments one or more of the lens portions utilized mayalternatively (or additionally) include a powered lens, such as a VFL5400 as described in the present disclosure. Based on calculations andmodeling, it is believed that a beam steering device such as thatdepicted in FIGS. 62 and 63 is capable to steer an incident EM beam toan angle exceeding +/−20°, and/or exceeding +/−30°.

Referencing FIG. 63, another embodiment of a beam steering device isdepicted, with separated components for the convex lens portion 6302 andthe concave lens portion 6304. In certain embodiments, the separation ofthe lens portions 6302, 6304 may provide for ease of fabrication, easeof cooling and/or electrical connections to the thin beam steeringdevice 6206, and/or separation of the lens portions 6302, 6304 asdistinct devices and/or having distinct operating configurations. Incertain embodiments, for example where the lens portions 6302, 6304 arean integrated component (e.g., as in FIG. 62) and/or manufactured by thesame processes, aberrations in the lens portions may acceptably offset.In certain embodiments, manufacturing tolerances may be utilized toensure acceptable performance of the lens portions 6302, 6304.

Referencing FIG. 64, a schematic diagram of a beam steering device 6400utilizing a concave emission surface 5902 and a varifocal lens 5400 isdepicted. In the example of FIG. 64, a number of triangular high-sideelectrodes 6404 are depicted, creating a number of steering portions ofthe beam steering device 6400. The example beam steering device 6400further includes a number of low-side electrodes 6402 on the back sideof the beam steering device 6400 opposite the high-side electrodes 6404.An example device may include a low-side electrode 6402 corresponding toeach of the high-side electrodes 6404, and/or may include a commonlow-side electrode or other configurations as set forth throughout thepresent disclosure. The example beam steering device 6404 includes anincreasing size of the bulk crystal (e.g., increasing height of thecrystal from the VFL 5400 inlet to the concave face 5902 outlet), whichmay be monotonically increasing or in other configurations according tothe steered trajectory of the EM beam, physical and/or manufacturingconstraints of the device, or the like. In certain embodiments, the VFL5400 may be omitted, for example when the divergence induced by theconcave face 5902 is acceptable over a range of steering angles, and/orwhen a fixed geometry (e.g., conventional lens) provides for sufficientconvergence of the steered EM beam through an acceptable range ofsteering angles for a particular application.

According to modeling and calculations, it is believed that a beamsteering device 6400 is capable to steer an incident EM beam at anglesgreater than +/−30 with minimal divergence of the EM beam in a singledimension (or axis). The beam steering device 6400 is capable to steeran incident EM beam at even greater angles with some divergence, whichmay be acceptable for certain applications. The steering portions of thebeam steering device 6400 are depicted as steering in a single dimensionfor the embodiments described herein, but the beam steering device 6400may additionally or alternatively include steering in two dimensions,for example with adjustments as set forth in FIGS. 37, 39, and 59 andthe related descriptions. The concave face 5902 depicted in FIG. 64 iscurved in only a single dimension, but may similarly be curved in morethan one dimension, for example as set forth in FIGS. 59, 61, and therelated descriptions.

Certain illustrative operating principles for a beam steering device6400 including a concave face 5902 and a VFL 5400 are described herein.The example operating principles are provided for clarity of the presentdescription, and are not limiting to the embodiments described herein.Additionally, while certain operating principles are described in thecontext of the embodiment of FIG. 64, the descriptions herein may beapplicable to any of the embodiments described herein. One of skill inthe art, having the benefit of the present disclosure and informationordinarily available when contemplating a particular system, includingmaterials available, manufacturing techniques that are commerciallyreasonable, and steering requirements or desired characteristics for aparticular system and application, can readily determine theconfiguration of a beam steering device to implement embodiments herein.

An example beam steering device 6400 such as that depicted in FIG. 64 iscapable to continuously steer an incident EM beam 5602 to wide angles(e.g., +/−30°, and greater depending upon the amount of divergence thatis acceptable for a particular system and/or application). The examplebeam steering device 6400 takes advantage of the index mis-match betweenthe crystal material and air to magnify the steering angle of theoutgoing beam. The average path length through the scanner changes theincident EM beam is steered, so even though the exit optical element isfixed, a VFL can be utilized to reduce or minimize distortion (e.g., vianet divergence or convergence) of the steered EM beam.

The EO bulk scanner 6400 includes an input with a VFL attached (and/oroptically coupled) to a bulk EO crystal, followed by several triangularelectrodes on two opposite sides of a gradually widening bulk EOcrystal, and ending with the EO crystal having a concave surface, whichmay resemble a fishtail. In certain embodiments, the bulk EO crystalscanner 6400 is referenced as a Fishtail scanner. The number and shapeof the triangular electrodes are designed in consideration of a tradeoffbetween maximum deflection angle and the maximum acceptable insidereflection. A larger number of triangular electrode will lead to a widerdeflection angle because it provides more prisms on the pathway of thelight, but also it will create more internal changes in index ofrefraction, or interfaces. Having more internal interfaces reduces thedeflection efficiency because a fraction of light will be reflected ateach interface. The shape of each triangular electrode may be designedby ray tracing to avoid hitting the wall when the maximum voltage isapplied. As the width of the Fishtail scanner crystal graduallyincreases, the triangular electrodes become narrower because there willbe more room for deflection of light without hitting the wall.

The exit surface of the Fishtail scanner is curved, and therefore hasoptical power. Without compensation the deflected beam coming out of thescanner would be diverging. To compensate the optical power of thatcurved surface, the VFL applies a convergence to the incident EM beam.In certain embodiments, a fixed compensation lens may be utilized at theinput, for example where variance imposed by the changing effective pathlength between the Fishtail scanner inlet and outlet is acceptable for aparticular application.

An example design equation for the optical power of the varifocal lens(ϕ_(vl)) follows in equation 11:

$\begin{matrix}{\phi_{vl} = {\frac{1}{f} = {\frac{s_{ij}n_{0}^{3}V_{0}^{2}}{L^{2}d_{0}} = {\frac{n_{0}^{3}V_{0}^{2}g_{ij}{ɛ(T)}^{2}}{L^{2}d_{0}} = {{\frac{V_{0}^{2}{ɛ(T)}^{2}}{K}\mspace{14mu} T} > T_{c}}}}}} & {{EQ}.\mspace{14mu} 11}\end{matrix}$

Where d₀ is the path length without any index change, n₀ is the ordinaryrefractive index of the crystal, V₀ is the voltage applied, T istemperature, Tc is the Curie temperature, L is the distance across thebulk crystal (e.g. reference FIGS. 66-69). In the case of KTN (KT/KN, orpotassium tantalate/potassium niobite), the optical power of thevariable lens is set forth in equation 12:

$\begin{matrix}{\phi_{vl} = {\frac{1}{f} = {{\frac{V_{0}^{2}}{K}\left( \frac{140000ɛ_{0}}{T - T_{c}} \right)^{2}\mspace{14mu} T} > T_{c}}}} & {{EQ}.\mspace{14mu} 12}\end{matrix}$

The power of the curved outlet surface of the fishtail (ϕ_(cs)) undervoltage of V is set forth in equation 13:

$\begin{matrix}{\phi_{cs} = \frac{{n(V)} - 1}{R}} & {{EQ}.\mspace{14mu} 13}\end{matrix}$

Where R is the curvature radius of the outlet surface (which may be alocal curvature) and n(V) is the refractive index of the crystal whichis a function of the applied voltage (V) on the crystal as follows inequations 14 (paraelectric region) and 15 (ferroelectric region):

$\begin{matrix}{{n(V)} = {n - \frac{0.5n^{3}g_{ij}{ɛ(T)}^{2}V^{2}}{d^{2}}}} & {{EQ}.\mspace{14mu} 14} \\{{n(V)} = {n - \frac{0.5n^{3}r_{ij}V}{d}}} & {{EQ}.\mspace{14mu} 15}\end{matrix}$

Where n is the index of the scanner, n³ g_(ij) is the quadraticelectro-optical constant, ε(T) is the dielectric constant as a functionof temperature, V is the applied voltage on the scanner, r_(ij) is thelinear electro-optical constant of the crystal and d is the thickness ofthe scanner.

Calculation of the total optical power between two surfaces having adistance therebetween is discussed in J. E. Greivenkamp, “Field guide togeometrical optics,” SPIE, 2004, pp. 14, which is incorporated herein byreference. If the length of the Fishtail scanner is t, the total opticalpower of the scanner is set forth in equation 16:

$\begin{matrix}{\phi = {{\phi_{vl} + \phi_{cs} - \frac{\phi_{vl}\phi_{cs}t}{n(V)}} = {\frac{V_{0}^{2}{ɛ(T)}^{2}}{K} + \frac{{n(V)} - 1}{R} - \frac{{tV}_{0}^{2}{ɛ(T)}^{2}\left( {{n(V)} - 1} \right)}{{n(V)}{KR}}}}} & {{EQ}.\mspace{14mu} 16}\end{matrix}$

It should be noted again that the VFL is under a first voltage (e.g.,V_(o)) and the bulk crystal portion of the scanner is under a secondvoltage (e.g., V). It will be understood that different steeringportions of the bulk crystal portion of the scanner may be underdistinct voltages, and equation 16 may be modified to compensate for thevarying voltage portions of the scanner. For the fixed temperature (T)and given voltage on the scanner (V), (or given angle of deflection),the total power of the scanner (ϕ) can be plotted against the appliedvoltages on the VFL to find the desired V₀ in which the total power ofthe scanner (ϕ) is minimum. It is understood that other constraints ofthe system may indicate a V₀ that does not correspond to the minimumtotal power of the scanner, but equation 16 can be utilized to improveand/or minimize the total power of the scanner, and/or to determinesensitivity of the total power of the scanner to design and/or run-timeparameters. Because of the power of the VFL (ϕ_(vl)), the voltageapplied on the VFL (V_(o)) can be adjusted to compensate for the opticalpower of the exit curved surface (ϕ_(cs)).

Without using the VFL, the power of the scanner will be

$\phi_{cs} = \frac{{n(V)} - 1}{R}$which results in a diverging deflected beam. By employing that VFL, thebeam can be steered to a wide angle without diverging the steered beam.If the application allows having a diverging deflected beam, the VFL canbe omitted and/or replaced with a fixed power lens.

The VFL operates like a cylindrical graded-index lens. Generally, agraded-index lens is a thin plate of uniform thickness d₀ andquadratically graded refractive index n(x, y)=n₀[1−0.5α²(x²+y²)], whereα is a parameter in terms of m⁻¹ that relates the index to every pointof the crystal with dimension of (x,y). The αd₀ is dimensionless and Ifαd₀<<1, acts as a lens of focal length

$f = \frac{1}{n_{0}d_{0}\alpha^{2}}$(e.g., see B. E. A. Saleh and M. C. Teich, “Fundamentals of Photonics,”2nd Edition, John Wiley & Sons, Inc. 2015, pp. 57, which is incorporatedby reference herein).

In the case of a cylindrical graded-index lens, the index changes in onedirection only, following equation 17:Δn(x)=n(x)−n ₀=−0.5n ₀α² x ²  EQ. 17:

As seen in equation 17, if the index of the thin plate of uniformthickness d₀ gradually changes by x², that plate will behave like acylindrical lens. In Kerr effect bulk crystals under voltage of V, therefractive index of the crystal is varied in terms of V². Therefore, athin plate of the Kerr effect bulk crystal can form a cylindrical lensif the applied voltage is linearly varied with respect to x.

Referencing FIG. 65, the VFL includes a thin plate of an electro-optical(EO) crystal with a uniform thickness of d₀. In the example of FIG. 65,L 6508 is the distance between the electrodes. Example thin platematerials include any EO crystals with a sizeable Kerr effect, such asKTN or PMNPT.

In an example, two different voltages are applied on the electrodes, andthe uniform transparent electrode at the backside of the crystal isconnected to the ground. Assuming voltages of V_(o) and zero arerespectively applied on the first and second electrode, the distributionof the electric field in the crystal is set forth in equation 18:

$\begin{matrix}{{E(x)} = {\frac{dV}{dy} = {{\frac{V_{0}x}{{Ld}_{0}}\mspace{14mu} 0} \leq x \leq L}}} & {{EQ}.\mspace{14mu} 18}\end{matrix}$

Accordingly, the index change caused by the Kerr effect is set forth inequation 19:Δn(x)=n(x)−n ₀=−0.5n ₀ ³ s _(ij) E(x)²  EQ. 19:

Where n₀ is the index of the crystal before applying any voltage. If theincident light is polarized perpendicular to the crystal axis, the n₀will be the ordinary index, otherwise n₀ is the extraordinary index ofthe crystal. The s_(ij) is the appropriate element of the Kerr effecttensor, which is related to the dielectric constant of the crystal asset forth in equation 20:s _(ij) =g _(ij)ε(T)²  EQ. 20:

Where g_(ij) is the appropriate electrostrictive tensor element, and εis the dielectric constant, which is a function of temperature. In thecase of KTN, the dielectric constant as a function of temperature is setforth in equation 21:

$\begin{matrix}{{ɛ(T)} = {{\frac{140000ɛ_{0}}{T - T_{c}}\mspace{14mu} T} > T_{c}}} & {{EQ}.\mspace{14mu} 21}\end{matrix}$

Where ε₀ is the dielectric constant in vacuum and T_(c) is the curietemperature of KTN. It should be noted that KTN exhibits a significantKerr effect at its paraelectric region. Therefore, the temperature ofthe crystal in certain embodiments is maintained higher than its Curietemperature. Accordingly, the index change in the VFL is set forth inequation 22:

$\begin{matrix}{{\Delta\;{n(x)}} = {{{- 0.5}s_{ij}n_{0}^{3}{E(x)}^{2}} = {{{- 0.5}s_{ij}n_{0}^{3}\frac{V_{0}^{2}}{L^{2}d_{0}^{2}}x^{2}\mspace{14mu} 0} \leq x \leq L}}} & {{EQ}.\mspace{14mu} 22}\end{matrix}$

Referencing FIGS. 70 and 71, the voltage and index change across thelength of a 6 cm×6 cm×1 mm KTN crystal plate under 5 kV are plotted.Note that the voltage range goes from −5 Kv to +5 Kv. In the middle, thevoltage is zero, so there is no index change, as seen in FIG. 71. InFIG. 71, it apparent that the index change varies from −0.3 throughzero, and back to −0.3. As seen in equation 16 and FIG. 71, the indexchange is a function of x². Hence, the thin plate of the Kerr effectcrystal forms a cylindrical graded index lens in one dimension. Thefocal length of the VFL is set forth in equation 23:

$\begin{matrix}{f = {\frac{L^{2}d_{0}}{s_{ij}n_{0}^{3}V_{0}^{2}} = {\frac{L^{2}d_{0}}{n_{0}^{3}V_{0}^{2}g_{ij}{ɛ(T)}^{2}} = {{\frac{K}{V_{0}^{2}{ɛ(T)}^{2}}\mspace{14mu} T} > T_{c}}}}} & {{EQ}.\mspace{14mu} 23}\end{matrix}$

Where

$K = \frac{L^{2}d_{0}}{n_{0}^{3}g_{ij}}$is a constant because the L and d₀ are the geometry parameters, and n₀and g_(ij) are material properties. Of course n₀ and g_(ij) depend onthe wavelength and polarization of the incident EM beam, but they areconstant for given incident EM beam.

The focal length can be altered by changing the applied voltage of V₀ orchanging the dielectric constant by varying the temperature. In the caseof KTN, as the Kerr effect crystal, the focal length and optical powerof the variable lens as a function of temperature and the appliedvoltage is set forth in equations 24 and 25:

$\begin{matrix}{f = {{\frac{K}{V_{0}^{2}}\left( \frac{T - T_{c}}{140000ɛ_{0}} \right)^{2}\mspace{14mu} T} > T_{c}}} & {{EQ}.\mspace{14mu} 24} \\{\phi = {{\frac{V_{0}^{2}}{K}\left( \frac{140000ɛ_{0}}{T - T_{c}} \right)^{2}\mspace{14mu} T} > T_{c}}} & {{EQ}.\mspace{14mu} 25}\end{matrix}$

As seen, the focal length and power of the varifocal lens are sensitiveto temperature and the applied voltage. When no voltage is applied, orthe temperature is high, the varifocal lens does not have optical power.In contrast, when applied voltage is high and/or the temperature isclose to the Curie temperature, the optical power is configurable andcan be very high. It should be noted that, to achieve a high power lensor a lens with a short focal length, the temperature can be adjustedclose to the Curie temperature rather than applying a very high voltage.Referencing FIGS. 66, 67, and 69, simulated results are depicted for abeam steering device having a VFL made of KTN with a length of 5 mm, anda thickness of 1 mm. For reference, it is noted that KTN has a T_(c) of300K, and an n³g₁₁ of 2 m⁴/C².

Referencing FIG. 72, an example VFL response is shown with thetemperature is fixed at 308K, and the voltage varied from 0 to 5 kV.Referencing FIG. 73, an example VFL response is shown with the voltagefixed at 5 kV, and the temperature varied from 308K to 500K. It is shownthat the focal length will be small for high applied voltage and/or lowtemperature. Accordingly, in certain embodiments, the temperature of theVFL is kept close to the Curie temperature, allowing for a high opticalpower to be achieved with a lower voltage applied.

Referencing FIG. 65, a schematic diagram of an example VFL 5400suitable, for example, for utilization with a beam steering device 6400is depicted. The example VFL 5400 includes high-side electrodes 6502positioned on each side of the VFL viewing area (e.g., the area throughwhich an incident EM beam is designed to progress), and a low-sideelectrode 6504 positioned on an opposite side of the VFL. In theexample, the high-side electrodes 6502 may be positioned outside the VFLviewing area, and/or may be provided as transparent electrodes. In theexample of FIG. 65, the low-side electrode 6504 is provided to cover theVFL viewing area, and is a transparent electrode. In certainembodiments, voltages are applied to the high-side electrodes 6502 toprovide a voltage gradient across the bulk crystal 6506 of the VFL. Incertain embodiments, the high-side electrodes are provided with voltagesof equal magnitude and opposite sign, providing a voltage gradientacross the distance 6508 of the VFL having a zero point in the center ofthe VFL. In the example of FIG. 65, the bulk crystal 6506 is maintainedabove a Curie temperature, and operates in the Kerr effect(paraelectric) region, which exhibits a quadratic voltage gradient. Itcan be seen that the VFL 5400 acts as a lens in a single dimension,tending to converge the incident EM beam. In certain embodiments, theVFL 5400 can be operated as a two-dimensional (or spherical lens), forexample utilizing a closed surface or round high-side electrode, and/orutilizing additional high-side electrodes (e.g., across the top andbottom, or other dimension of the VFL bulk crystal). In certainembodiments, the VFL 5400 can be utilized as a lens in two dimensionswith two staged VFLs 5400 utilized in series.

During operations of the beam steering device 6400, the VFL 5400 (and/ora conventional lens) applies a converging effect to the incident EM beam5602. The incident EM beam is then passed through the number of steeringportions of the beam steering device 6400, each one of the steeringportions incrementally steering the EM beam toward the target steeringamount (e.g., a steering request value and/or a steering command value).Upon emission of the steered EM beam through the concave face 5902, theconcave face 5902/medium (e.g., air) interface effectively multipliesthe amount of steering performed. Accordingly, in certain embodiments,the steering request value and/or steering command value is convertedinto a target position of the steered EM beam onto the concave face5902, target index values (and/or voltage values) of the steeringportions, and/or a target focal length of the VFL 5400 to apply aselected amount of convergence. The amount of convergence may bescheduled according to the steering amount applied, the curvature of theconcave face 5902 at the point where the steered EM beam is emitted, thedistance to the steering target of the steered EM beam, or the like. Incertain embodiments, feedback about the amount of divergence may beavailable (e.g., determining how much of the EM beam energy is deliveredeffectively to a target), and the VFL 5400 may modulate the convergenceamount to achieve a target effective divergence amount at a selectedposition (e.g., the target distance, a selected nominal distance, etc.).

The bulk crystal, including the beam steering portions, of the beamsteering device 5400 may be operated either in the paraelectric,ferroelectric, Kerr effect, or Pockels effect EO operating regions. Incertain embodiments, some of the beam steering portions may be operatedin one EO operating region, and other ones operated in the other EOoperating region. In certain embodiments, as described preceding, thetemperature of the VFL 5400 and/or the bulk crystal may affect theamount of steering and/or focal length of the VFL 5400. Accordingly, incertain embodiments, one or more temperatures in the beam steeringdevice 6400 may be detected (e.g., utilizing a sensor, temperaturemodel, and/or other value from which temperature can be determined orinferred), and the voltage values for the VFL 5400 and/or one or moresteering portions may be compensated to achieve the desired opticalcharacteristics. In certain embodiments, one or more temperatures in thebeam steering device 5400 may be actively (e.g., with thermal contact toa coolant, thermoelectric device, or the like) and/or passivelycontrolled to maintain either target temperatures and/or temperaturebounds (e.g., ensuring that the appropriate Kerr effect or Pockelseffect is maintained).

Referencing FIGS. 66-69, a number of depictions of illustrativeperformance of a beam steering device consistent with certainembodiments of the present disclosure are presented. Referencing FIG.66, an incident EM beam 5602 is steered to about 15 degrees, and adivergence amount of the steered EM beam 6602 is minimal. The embodimentof FIG. 66 is believed, based upon calculations and modeling, to bereadily achievable for a beam steering device 6400 having a concavesurface 5902 at the emission end, with a VFL 5400 applying a convergenceto the EM beam 5602 at the receiving end. Referencing FIG. 67, anincident EM beam 5602 is steered to about 23 degrees, and a divergenceamount of the steered EM beam 6602 remains very low. The embodiment ofFIG. 67 is believed, based upon calculations and modeling, to be readilyachievable for a beam steering device 6400 having a concave surface 5902at the emission end, with a VFL 5400 applying a convergence to the EMbeam 5602 at the receiving end. Referencing FIGS. 68 and 69, an incidentEM beam 5602 is steered to about 43 degrees. The embodiment of FIG. 68depicts a beam steering device 6400 without a VFL 5400, and theembodiment of FIG. 69 depicts a beam steering device 6400 having a VFL5400. The embodiment of FIG. 69 has a much lower divergence of thesteered EM beam 6602 than the embodiment of FIG. 68, but it can be seenthat both devices are capable to steer the EM beam 6602 to a very largeangle. The embodiments of FIGS. 68 and 69 are believed, based uponcalculations and modeling, to be readily achievable for beam steeringdevices 6400 as described herein.

Referencing FIG. 70 is a depiction of illustrative design or controlcharacteristics of a varifocal lens 5400. The example of FIG. 70 depictsthe voltage profile across the VFL 5400 with a −5000V applied to a firstone of the high-side electrodes, and a +5000V applied to the second oneof the high-side electrodes. It can be seen that the voltage through theVFL 5400 in the example is a linear voltage gradient. Referencing FIG.71, the relative index change across the VFL 5400 is depicted in thepresence of the voltage gradient of FIG. 70 at a selected temperature.The data such as that depicted in FIGS. 70 and 71 is readily availableor determinable by one of skill in the art contemplating a particularsystem and beam steering device 6400, and can be utilized in the designand/or control of the device. At design time, the data such as in FIGS.70 and 71 can be utilized to select suitable EO materials, sizing,electrical characteristic design (e.g., power source, connections,insulation, etc.). At run time, the data such as in FIGS. 70 and 71 maybe available to a controller, and utilized to apply selected voltagegradients, compensate for actual temperatures, and the like. The exampleof FIG. 72 depicts the VFL 5400 focal length versus applied voltage fora particular VFL 5400, and can similarly be utilized at design time orrun-time to configure and/or operate a VFL 5400 for a beam steeringdevice 6400. The example of FIG. 73 depicts the VFL 5400 focal lengthversus temperature for a particular VFL 5400 at a selected voltage(5000V in the example), and can similarly be utilized at design time orrun-time to configure and/or operate a VFL 5400 for a beam steeringdevice 6400. Additionally or alternatively, data for the bulk crystal ofthe beam steering device 6400 may be utilized to design and/or controlthe steering portions. Data such as that depicted in FIGS. 70-73 may beavailable to a controller of the beam steering device 6400 in anyformat, such as look-up tables and/or models.

Referencing FIG. 74 is a schematic diagram of a system for beam steeringincluding a concave emission surface and a varifocal lens. The examplesystem includes a beam steering device 6400, including a number ofsteering portions, and which may further include a VFL at an inlet endof the device where an incident EM beam is received for steering. Theexample system further includes a concave face at an emission end wherethe steered EM beam is emitted. The example system includes a bulkcrystal temperature sensor 7402, which may be any device and/or model(or virtual sensor) that provides a temperature value indicative of atemperature of one or more of the steering portions of the beam steeringdevice 6400. The example system includes a VFL temperature sensor 7406that provides a temperature value indicative of a temperature of the VFLsubstrate (bulk crystal portion of the VFL). The example system includesa controller 7408 which is communicatively coupled to one or moreaspects of the system, such as sensors, actuators, externalcommunications or control devices, or the like. In certain embodiments,the controller 7408 is configured to control voltages across electrodesof the beam steering portions and/or the VFL, to determine steeringrequests or commands, to determine characteristics of the incident EMbeam to the beam steering device, and the like. Embodiments of thecontroller 7408 may include aspects of any of the controllers and/orcircuits described throughout the present disclosure. The controller7408 may be positioned on a single device, for example as a processor,memory, and/or computer executable code which, when executed, causes thecontroller 7408 to perform operations related to the beam steeringdevice 6400. In certain embodiments, aspects of the controller 7408 maybe distributed across a number of devices. In certain embodiments, thecontroller 7408 may communicate with other devices, such as a voltagecontroller or other actuator, and may control actuators in the systemutilizing electrical commands (e.g., applying a voltage to a steeringportion), communications (e.g., commanding a voltage controller to applya voltage to a steering portion), and/or combinations of these.

Referencing FIG. 75, an example controller 7408 for controlling a beamsteering device is depicted. The example controller 7408 includes a beamsteering circuit 7502 structured to adjust a voltage drop 7506 acrosssteering portions of a beam steering device. In certain embodiments, thebeam steering circuit 7502 determines a steering request value 7504, andadjusts the voltage drop(s) 7506 to implement steering of an incident EMbeam in response to the steering request value 7504. In certainembodiments, the beam steering circuit 7502 provides appropriatecommands to a voltage controller 7508 to implement the voltage drop(s)7506, for example by providing voltage commands, index commands, and/orsteering amount commands for one or more of the steering portions, tothe voltage controller 7508. In certain embodiments, the beam steeringcircuit 7502 is further structured to adjust a focal length 7510 of aVFL in response to the steering request value 7504. In certainembodiments, the example controller 7408 may operate a beam steeringdevice such as the device(s) depicted in FIG. 32, 56, 57, or 64, and therelated descriptions.

Referencing FIG. 76, an example controller 7408 for controlling a VFL isdepicted. The example controller 7408 includes a VFL circuit 7602structured to adjust a voltage gradient 7610 across a bulk substrate ofa VFL, and thereby operate the bulk substrate as a VFL. In certainembodiments, the VFL circuit 7602 determines a convergence value 7604,for example to compensate for a divergence effect in a system of a beamsteering device, and determines the voltage gradient 7610 in response tothe convergence value 7604. In certain embodiments, the VFL circuit 7602determines a focal length 7614 for the VFL, and determines the voltagegradient 7610 in response to the determined focal length 7614. Incertain embodiments, the VFL circuit 7602 determines the convergencevalue 7604 and/or the focal length 7614 in response to a steering angle7606 (e.g., accounting for divergence from the steering and/or from anemission through a concave face of a beam steering device) and/or inresponse to an incident angle 7608 of the incident EM beam. In certainembodiments, the VFL circuit 7602 provides the voltage gradient 7610 byproviding commands to a voltage controller 7612, for example byproviding voltage commands, index commands, and/or focal lengthcommands, to the voltage controller 7612.

Referencing FIG. 77, an example controller 7408 includes a bulk steeringcircuit 7702 structured to interpret a steering command value 7504(e.g., a location and/or steering angle for the incident EM beam), andto provide a voltage commands 7708 to high-side electrodes of a beamsteering device 6400 in response to the steering command value 7504. Forexample, the bulk steering circuit 7702 may receive the steering commandvalue 7504, and apply a steering trajectory across the beam steeringportions to steer the incident EM beam in accordance with the steeringcommand value 7504. An example bulk steering circuit 7702 furtherprovides low-side voltage commands (e.g., as a part of the voltagecommands 7708) to low-side electrodes of the beam steering device—forexample where the both the high-side and low-side electrodes areoperated at a voltage to provide for the scheduled voltage differentialfor a given steering portion. In certain embodiments, the high-sideelectrodes and low-side electrodes may be operated at the same voltagemagnitude, with opposite signs, to enhance the voltage differentialwhile minimizing the magnitude of the operating voltages in the beamsteering device 6400. In certain embodiments, the low-side electrodesmay be operated as ground electrodes, and/or may be operated at a lower,or negative, voltage relative to the high-side electrodes, but not witha same magnitude as the voltage of the high-side electrodes. In certainembodiments, it may be desirable to operate the high-side electrodes ata similar voltage, to progressively steer the beam and to minimizevoltage differences between adjacent steering portions, but thehigh-side electrodes may be operated at any voltage including distinctand/or highly varying voltages. In certain embodiments, steering controlmay be simplified if only a portion of the available steering portionsare activated (e.g., when a small steering angle is being implemented),and accordingly the high-side electrode voltages may be varied.

The example controller 7408 further includes a VFL circuit 7602structured to provide a voltage gradient 7610 command in response to thesteering command value 7504. In certain embodiments, the VFL isresponsive to the voltage gradient 7610 command (e.g., in response to avoltage controller applying a voltage in accordance with the voltagegradient 7610 command), thereby applying a lensing effect to theincident EM beam at a selected focal length. The example VFL circuit7602 may command voltages to the high-side electrodes, and/or commandvoltages to the low-side electrode. In certain embodiments, the VFLcircuit 7602 determines a beam divergence value 7612, for exampledetermined in response to the steering command value 7504, and/ordetermined in response to a curvature of or divergence incurred by theconcave face 5902 of the beam steering device (including potentially atthe targeted steering location), and to further provide the voltagegradient 7610 command in response to the beam divergence value 7612. Anexample VFL circuit 7602 further determines a VFL temperature value7704, and further determines the voltage gradient 7610 command inresponse to the VFL temperature value 7704. An example bulk steeringcircuit 7702 further determines one or more bulk crystal temperaturevalues 7706, and further provides the voltage command(s) 7708 inresponse to the bulk crystal temperature value(s) 7706. In certainembodiments, the bulk steering circuit 7702 may adjust high-sideelectrode voltage commands and/or low-side electrode voltage commands inresponse to the bulk crystal temperature value(s) 7706.

Referencing FIG. 78, an example procedure 7800 for steering an incidentEM beam is depicted. The example procedure 7800 includes an operation7802 to determine a divergence value of an incident EM beam (e.g., asemitted from the beam steering device), and an operation 7806 to apply aselected convergence amount to an incident EM beam (e.g., utilizing aVFL). In certain embodiments, the procedure 7800 includes an operation7804 to compensate the selected convergence amount in response to thedivergence value. The example procedure 7800 further includes anoperation 7808 to progressively steer the incident EM beam throughsteering portions of a bulk steering crystal, and an operation 7810 toemit the incident EM beam from a concave face of the bulk steeringcrystal.

Referencing FIG. 79, an example procedure 7806 for operating a VFL toapply a selected convergence amount, and/or to implement a target focallength, is depicted. The example procedure 7806 includes an operation7902 to determine a nominal voltage gradient to implement a selectedconvergence amount and/or a target focal length for the VFL. The exampleprocedure 7806 further includes an operation 7904 to determine whether aVFL temperature value indicates that voltage compensation for the VFL isindicated. In response to operation 7904 determining YES, the exampleprocedure 7806 includes an operation 7906 to adjust the voltage gradientin response to a temperature of the VFL, and an operation 7908 to applythe compensated voltage gradient to the VFL. In response to operation7904 determining NO, the example procedure 7806 includes the operation7908 to apply the voltage gradient to the VFL.

Referencing FIG. 80, an example procedure 7808 to apply voltagedifferential to a number of steering portions of a beam steering deviceis depicted. The example procedure 7808 includes an operation 8002 todetermine voltage differentials for each steering portion of the beamsteering device, and an operation 8004 to determine whether bulk crystaltemperature(s) indicate that voltage compensation for one or moresteering portions should be provided. In response to operation 8004indicating YES, the procedure 7808 includes an operation 8006 tocompensate one or more of the voltage differentials in response to thebulk crystal temperature(s), and an operation 8008 to apply thecompensated voltage differentials to each of the steering portions. Inresponse to operation 8004 indicating NO, the procedure 7808 includes anoperation 8006 to apply the voltage differentials to each of thesteering portions.

The methods and systems described herein may be deployed in part or inwhole through a machine having a computer, computing device, processor,circuit, and/or server that executes computer readable instructions,program codes, instructions, and/or includes hardware configured tofunctionally execute one or more operations of the methods and systemsherein. The terms computer, computing device, processor, circuit, and/orserver, (“computing device”) as utilized herein, should be understoodbroadly.

An example computing device includes a computer of any type, capable toaccess instructions stored in communication thereto such as upon anon-transient computer readable medium, whereupon the computer performsoperations of the computing device upon executing the instructions. Incertain embodiments, such instructions themselves comprise a computingdevice. Additionally or alternatively, a computing device may be aseparate hardware device, one or more computing resources distributedacross hardware devices, and/or may include such aspects as logicalcircuits, embedded circuits, sensors, actuators, input and/or outputdevices, network and/or communication resources, memory resources of anytype, processing resources of any type, and/or hardware devicesconfigured to be responsive to determined conditions to functionallyexecute one or more operations of systems and methods herein.

Network and/or communication resources include, without limitation,local area network, wide area network, wireless, internet, or any otherknown communication resources and protocols. Example and non-limitinghardware and/or computing devices include, without limitation, a generalpurpose computer, a server, an embedded computer, a mobile device, avirtual machine, and/or an emulated computing device. A computing devicemay be a distributed resource included as an aspect of several devices,included as an interoperable set of resources to perform describedfunctions of the computing device, such that the distributed resourcesfunction together to perform the operations of the computing device. Incertain embodiments, each computing device may be on separate hardware,and/or one or more hardware devices may include aspects of more than onecomputing device, for example as separately executable instructionsstored on the device, and/or as logically partitioned aspects of a setof executable instructions, with some aspects comprising a part of oneof a first computing device, and some aspects comprising a part ofanother of the computing devices.

A computing device may be part of a server, client, networkinfrastructure, mobile computing platform, stationary computingplatform, or other computing platform. A processor may be any kind ofcomputational or processing device capable of executing programinstructions, codes, binary instructions and the like. The processor maybe or include a signal processor, digital processor, embedded processor,microprocessor or any variant such as a co-processor (math co-processor,graphic co-processor, communication co-processor and the like) and thelike that may directly or indirectly facilitate execution of programcode or program instructions stored thereon. In addition, the processormay enable execution of multiple programs, threads, and codes. Thethreads may be executed simultaneously to enhance the performance of theprocessor and to facilitate simultaneous operations of the application.By way of implementation, methods, program codes, program instructionsand the like described herein may be implemented in one or more threads.The thread may spawn other threads that may have assigned prioritiesassociated with them; the processor may execute these threads based onpriority or any other order based on instructions provided in theprogram code. The processor may include memory that stores methods,codes, instructions and programs as described herein and elsewhere. Theprocessor may access a storage medium through an interface that maystore methods, codes, and instructions as described herein andelsewhere. The storage medium associated with the processor for storingmethods, programs, codes, program instructions or other type ofinstructions capable of being executed by the computing or processingdevice may include but may not be limited to one or more of a CD-ROM,DVD, memory, hard disk, flash drive, RAM, ROM, cache and the like.

A processor may include one or more cores that may enhance speed andperformance of a multiprocessor. In embodiments, the process may be adual core processor, quad core processors, other chip-levelmultiprocessor and the like that combine two or more independent cores(called a die).

The methods and systems described herein may be deployed in part or inwhole through a machine that executes computer readable instructions ona server, client, firewall, gateway, hub, router, or other such computerand/or networking hardware. The computer readable instructions may beassociated with a server that may include a file server, print server,domain server, internet server, intranet server and other variants suchas secondary server, host server, distributed server and the like. Theserver may include one or more of memories, processors, computerreadable transitory and/or non-transitory media, storage media, ports(physical and virtual), communication devices, and interfaces capable ofaccessing other servers, clients, machines, and devices through a wiredor a wireless medium, and the like. The methods, programs, or codes asdescribed herein and elsewhere may be executed by the server. Inaddition, other devices required for execution of methods as describedin this application may be considered as a part of the infrastructureassociated with the server.

The server may provide an interface to other devices including, withoutlimitation, clients, other servers, printers, database servers, printservers, file servers, communication servers, distributed servers, andthe like. Additionally, this coupling and/or connection may facilitateremote execution of instructions across the network. The networking ofsome or all of these devices may facilitate parallel processing ofprogram code, instructions, and/or programs at one or more locationswithout deviating from the scope of the disclosure. In addition, all thedevices attached to the server through an interface may include at leastone storage medium capable of storing methods, program code,instructions, and/or programs. A central repository may provide programinstructions to be executed on different devices. In thisimplementation, the remote repository may act as a storage medium formethods, program code, instructions, and/or programs.

The methods, program code, instructions, and/or programs may beassociated with a client that may include a file client, print client,domain client, internet client, intranet client and other variants suchas secondary client, host client, distributed client and the like. Theclient may include one or more of memories, processors, computerreadable transitory and/or non-transitory media, storage media, ports(physical and virtual), communication devices, and interfaces capable ofaccessing other clients, servers, machines, and devices through a wiredor a wireless medium, and the like. The methods, program code,instructions, and/or programs as described herein and elsewhere may beexecuted by the client. In addition, other devices required forexecution of methods as described in this application may be consideredas a part of the infrastructure associated with the client.

The client may provide an interface to other devices including, withoutlimitation, servers, other clients, printers, database servers, printservers, file servers, communication servers, distributed servers, andthe like. Additionally, this coupling and/or connection may facilitateremote execution of methods, program code, instructions, and/or programsacross the network. The networking of some or all of these devices mayfacilitate parallel processing of methods, program code, instructions,and/or programs at one or more locations without deviating from thescope of the disclosure. In addition, all the devices attached to theclient through an interface may include at least one storage mediumcapable of storing methods, program code, instructions, and/or programs.A central repository may provide program instructions to be executed ondifferent devices. In this implementation, the remote repository may actas a storage medium for methods, program code, instructions, and/orprograms.

The methods and systems described herein may be deployed in part or inwhole through network infrastructures. The network infrastructure mayinclude elements such as computing devices, servers, routers, hubs,firewalls, clients, personal computers, communication devices, routingdevices and other active and passive devices, modules, and/or componentsas known in the art. The computing and/or non-computing device(s)associated with the network infrastructure may include, apart from othercomponents, a storage medium such as flash memory, buffer, stack, RAM,ROM and the like. The methods, program code, instructions, and/orprograms described herein and elsewhere may be executed by one or moreof the network infrastructural elements.

The methods, program code, instructions, and/or programs describedherein and elsewhere may be implemented on a cellular network havingmultiple cells. The cellular network may either be frequency divisionmultiple access (FDMA) network or code division multiple access (CDMA)network. The cellular network may include mobile devices, cell sites,base stations, repeaters, antennas, towers, and the like.

The methods, program code, instructions, and/or programs describedherein and elsewhere may be implemented on or through mobile devices.The mobile devices may include navigation devices, cell phones, mobilephones, mobile personal digital assistants, laptops, palmtops, netbooks,pagers, electronic books readers, music players and the like. Thesedevices may include, apart from other components, a storage medium suchas a flash memory, buffer, RAM, ROM and one or more computing devices.The computing devices associated with mobile devices may be enabled toexecute methods, program code, instructions, and/or programs storedthereon. Alternatively, the mobile devices may be configured to executeinstructions in collaboration with other devices. The mobile devices maycommunicate with base stations interfaced with servers and configured toexecute methods, program code, instructions, and/or programs. The mobiledevices may communicate on a peer to peer network, mesh network, orother communications network. The methods, program code, instructions,and/or programs may be stored on the storage medium associated with theserver and executed by a computing device embedded within the server.The base station may include a computing device and a storage medium.The storage device may store methods, program code, instructions, and/orprograms executed by the computing devices associated with the basestation.

The methods, program code, instructions, and/or programs may be storedand/or accessed on machine readable transitory and/or non-transitorymedia that may include: computer components, devices, and recordingmedia that retain digital data used for computing for some interval oftime; semiconductor storage known as random access memory (RAM); massstorage typically for more permanent storage, such as optical discs,forms of magnetic storage like hard disks, tapes, drums, cards and othertypes; processor registers, cache memory, volatile memory, non-volatilememory; optical storage such as CD, DVD; removable media such as flashmemory (e.g. USB sticks or keys), floppy disks, magnetic tape, papertape, punch cards, standalone RAM disks, Zip drives, removable massstorage, off-line, and the like; other computer memory such as dynamicmemory, static memory, read/write storage, mutable storage, read only,random access, sequential access, location addressable, fileaddressable, content addressable, network attached storage, storage areanetwork, bar codes, magnetic ink, and the like.

Certain operations described herein include interpreting, receiving,and/or determining one or more values, parameters, inputs, data, orother information (“receiving data”). Operations to receive datainclude, without limitation: receiving data via a user input; receivingdata over a network of any type; reading a data value from a memorylocation in communication with the receiving device; utilizing a defaultvalue as a received data value; estimating, calculating, or deriving adata value based on other information available to the receiving device;and/or updating any of these in response to a later received data value.In certain embodiments, a data value may be received by a firstoperation, and later updated by a second operation, as part of thereceiving a data value. For example, when communications are down,intermittent, or interrupted, a first receiving operation may beperformed, and when communications are restored an updated receivingoperation may be performed.

Certain logical groupings of operations herein, for example methods orprocedures of the current disclosure, are provided to illustrate aspectsof the present disclosure. Operations described herein are schematicallydescribed and/or depicted, and operations may be combined, divided,re-ordered, added, or removed in a manner consistent with the disclosureherein. It is understood that the context of an operational descriptionmay require an ordering for one or more operations, and/or an order forone or more operations may be explicitly disclosed, but the order ofoperations should be understood broadly, where any equivalent groupingof operations to provide an equivalent outcome of operations isspecifically contemplated herein. For example, if a value is used in oneoperational step, the determining of the value may be required beforethat operational step in certain contexts (e.g. where the time delay ofdata for an operation to achieve a certain effect is important), but maynot be required before that operation step in other contexts (e.g. whereusage of the value from a previous execution cycle of the operationswould be sufficient for those purposes). Accordingly, in certainembodiments an order of operations and grouping of operations asdescribed is explicitly contemplated herein, and in certain embodimentsre-ordering, subdivision, and/or different grouping of operations isexplicitly contemplated herein.

The methods and systems described herein may transform physical and/oror intangible items from one state to another. The methods and systemsdescribed herein may also transform data representing physical and/orintangible items from one state to another.

The methods and/or processes described above, and steps thereof, may berealized in hardware, program code, instructions, and/or programs or anycombination of hardware and methods, program code, instructions, and/orprograms suitable for a particular application. The hardware may includea dedicated computing device or specific computing device, a particularaspect or component of a specific computing device, and/or anarrangement of hardware components and/or logical circuits to performone or more of the operations of a method and/or system. The processesmay be realized in one or more microprocessors, microcontrollers,embedded microcontrollers, programmable digital signal processors orother programmable device, along with internal and/or external memory.The processes may also, or instead, be embodied in an applicationspecific integrated circuit, a programmable gate array, programmablearray logic, or any other device or combination of devices that may beconfigured to process electronic signals. It will further be appreciatedthat one or more of the processes may be realized as a computerexecutable code capable of being executed on a machine readable medium.

The computer executable code may be created using a structuredprogramming language such as C, an object oriented programming languagesuch as C++, or any other high-level or low-level programming language(including assembly languages, hardware description languages, anddatabase programming languages and technologies) that may be stored,compiled or interpreted to run on one of the above devices, as well asheterogeneous combinations of processors, processor architectures, orcombinations of different hardware and computer readable instructions,or any other machine capable of executing program instructions.

Thus, in one aspect, each method described above and combinationsthereof may be embodied in computer executable code that, when executingon one or more computing devices, performs the steps thereof. In anotheraspect, the methods may be embodied in systems that perform the stepsthereof, and may be distributed across devices in a number of ways, orall of the functionality may be integrated into a dedicated, standalonedevice or other hardware. In another aspect, the means for performingthe steps associated with the processes described above may include anyof the hardware and/or computer readable instructions described above.All such permutations and combinations are intended to fall within thescope of the present disclosure.

While the disclosure has been disclosed in connection with certainembodiments shown and described in detail, various modifications andimprovements thereon will become readily apparent to those skilled inthe art. Accordingly, the spirit and scope of the present disclosure isnot to be limited by the foregoing examples, but is to be understood inthe broadest sense allowable by law.

What is claimed is:
 1. A system, comprising: a bulk steering crystalapparatus having: a first lens face and a second concave face; and aplurality of steering portions interposed between the first lens faceand the second concave face, wherein each of the plurality of steeringportions comprises: a bulk substrate portion comprising anelectro-optical material; and a corresponding high-side electrodeelectrically coupled to the corresponding one of the plurality ofsteering portions, wherein the bulk steering portions comprise anincreasing width in at least a steered axis.
 2. The system of claim 1,wherein each of the corresponding high-side electrodes are positioned ona side of the bulk steering crystal.
 3. The system of claim 2, furthercomprising a low-side electrode positioned on an opposing side of thebulk steering crystal to at least one of the corresponding high-sideelectrodes.
 4. The system of claim 2, wherein each of the correspondinghigh-side electrodes are positioned on a same side of the bulk steeringcrystal.
 5. The system of claim 4, further comprising a low-sideelectrode positioned on an opposing side of the bulk steering crystal.6. The system of claim 5, wherein the low-side electrode is positionedas the low-side electrode for a plurality of the steering portions. 7.The system of claim 5, wherein the low-side electrode is positioned asthe low-side electrode for all of the steering portions.
 8. The systemof claim 1, further comprising a bulk steering circuit structured tointerpret a steering command value, and to provide voltage commands toeach of the corresponding high-side electrodes in response to thesteering command value.
 9. The system of claim 8, further comprising: alow-side electrode positioned on an opposing side of the bulk steeringcrystal to at least one of the corresponding high-side electrodes; andwherein the bulk steering circuit is further structured to provide alow-side voltage command to the low-side electrode in response to thesteering command value.
 10. The system of claim 9, wherein the low-sidevoltage command comprises a negative voltage value, and wherein acorresponding high-side voltage command comprises a positive voltagevalue.
 11. The system of claim 10, wherein the low-side voltage commandcomprises a same magnitude as the corresponding high-side voltagecommand.
 12. The system of claim 1, further comprising a first portionof the plurality of steering portions configured to steer an incidentelectromagnetic (EM) beam in a first axis, and a second portion of theplurality of steering portions configured to steer the incident EM beamin a second axis.
 13. The system of claim 12, wherein the bulk substrateportions corresponding to the first portion of the plurality of steeringportions are oriented in a first direction, and wherein the bulksubstrate portions corresponding to the second portion of the pluralityof steering portions are oriented in a second direction.
 14. The systemof claim 13, wherein the bulk substrate portions corresponding to thefirst portion of the plurality of steering portions are traversed by theincident EM beam before the second portion of the plurality of steeringportions.
 15. The system of claim 12, wherein the bulk substrateportions corresponding to the first portion of the plurality of steeringportions are traversed by the incident EM beam before the second portionof the plurality of steering portions.
 16. The system of claim 15,further comprising at least one of an anti-reflective coating or ahalf-wave plate optically interposed between an interface of at leastone of the bulk substrate portions corresponding to the first portion ofthe plurality of steering portions and at least one of the bulksubstrate portions corresponding to the second portion of the pluralityof steering portions.
 17. The system of claim 12, wherein the concaveface comprises at least one shape selected from the shapes consistingof: a spherical cap; an ellipsoid cap; a hyperboloid cap; and anelliptic paraboloid cap.
 18. The system of claim 1, wherein the concaveface comprises at least one shape selected from the shapes consistingof: a circular cross-section; a parabolic cross-section; a hyperboliccross-section; and rotations of any one of the foregoing.
 19. The systemof claim 1, wherein the increasing width is monotonically increasingbetween the first lens face and the second concave face.
 20. The systemof claim 1, wherein the bulk substrate portions comprise a solidmaterial.
 21. A system, comprising: a bulk steering crystal apparatushaving: a first lens face and a second concave face; a plurality ofsteering portions interposed between the first lens face and the secondconcave face, wherein a first portion of the plurality of steeringportions are configured to steer an incident electromagnetic (EM) beamin a first axis, and a second portion of the plurality of steeringportions are configured to steer the incident EM beam in a second axis,wherein each of the plurality of steering portions comprises: a bulksubstrate portion comprising an electro-optical material, wherein thebulk substrate portions corresponding to the first portion of theplurality of steering portions are oriented in a first direction, andwherein the bulk substrate portions corresponding to the second portionof the plurality of steering portions are oriented in a seconddirection; and a corresponding high-side electrode electrically coupledto the corresponding one of the plurality of steering portions; and ananti-reflective coating optically interposed between an interface of atleast one of the bulk substrate portions corresponding to the firstportion of the plurality of steering portions and at least one of thebulk substrate portions corresponding to the second portion of theplurality of steering portions.
 22. A system, comprising: a bulksteering crystal apparatus having: a first lens face and a secondconcave face; a plurality of steering portions interposed between thefirst lens face and the second concave face, wherein each of theplurality of steering portions comprises: a bulk substrate portioncomprising an electro-optical material; and a corresponding high-sideelectrode electrically coupled to the corresponding one of the pluralityof steering portions; a bulk steering circuit structured to interpret asteering command value, and to provide voltage commands to each of thecorresponding high-side electrodes in response to the steering commandvalue; a varifocal lens (VFL) positioned at the first lens face; and aVFL circuit structured to provide a voltage gradient command in responseto the steering command value.
 23. The system of claim 22, wherein theVFL circuit is further structured to determine a beam divergence valuein response to the steering command value, and to provide the voltagegradient command further in response to the steering command value. 24.The system of claim 23, wherein the VFL circuit is further structured todetermine a VFL temperature value corresponding to the VFL, and toprovide the voltage gradient command further in response to the VFLtemperature value.
 25. The system of claim 22, wherein the VFLcomprises: a VFL substrate comprising an electro-optical material; atransparent low-side electrode positioned on a first side of the VFLsubstrate; and a high-side electrode positioned in electrical proximityto a second side of the VFL substrate.
 26. The system of claim 25,wherein the high-side electrode comprises a closed loop electrodepositioned on the second side of the VFL substrate.
 27. The system ofclaim 26, wherein the closed loop electrode comprises a symmetricallyclosed loop.
 28. The system of claim 26, wherein the closed loopelectrode comprises at least one of a circular electrode or anelliptical electrode.
 29. The system of claim 25, wherein the high-sideelectrode comprises a first high-side electrode positioned along a firstedge of a viewing area of the VFL substrate, and a second high-sideelectrode positioned along a second edge of the viewing area of the VFLsubstrate.
 30. The system of claim 29, wherein the first high-sideelectrode and the second high-side electrode are positioned outside anoptical path of the viewing area of the VFL substrate.
 31. The system ofclaim 29, wherein the first high-side electrode and the second high-sideelectrode are positioned within an optical path of the viewing area ofthe VFL substrate.
 32. The system of claim 31, wherein the firsthigh-side electrode and the second high-side electrode are transparent.33. The system of claim 29, wherein the VFL circuit is furtherstructured to provide the voltage gradient command by commanding a firstvoltage value to the first high-side electrode, and by commanding asecond voltage value to the second high-side electrode.
 34. The systemof claim 33, wherein the first voltage value and the second voltagevalue have an equal magnitude, and an opposite sign.
 35. The system ofclaim 33, wherein the VFL circuit is further structured to provide thevoltage gradient by commanding a third voltage value to the transparentlow-side electrode.
 36. The system of claim 25, wherein the VFLsubstrate comprises a solid material.
 37. A system, comprising: a bulksteering crystal apparatus having: a first lens face and a secondconcave face; a plurality of steering portions interposed between thefirst lens face and the second concave face, wherein each of theplurality of steering portions comprises: a bulk substrate portioncomprising an electro-optical material; and a corresponding high-sideelectrode electrically coupled to the corresponding one of the pluralityof steering portions; a bulk steering circuit structured to interpret asteering command value, and to provide voltage commands to each of thecorresponding high-side electrodes in response to the steering commandvalue, wherein the bulk steering circuit is further structured todetermine a bulk crystal temperature value corresponding to at least oneof the bulk steering portions, and to provide the voltage commands toeach of the corresponding high-side electrodes further in response tothe bulk crystal temperature value.
 38. The system of claim 37, furthercomprising: a low-side electrode positioned on an opposing side of thebulk steering crystal corresponding to the at least one of the bulksteering portions; and wherein the bulk steering circuit is furtherstructured to provide a low-side voltage command to the low-sideelectrode in response to the steering command value and the bulk crystaltemperature value.
 39. A system, comprising: a bulk steering crystalapparatus having: a first lens face and a second concave face; aplurality of steering portions interposed between the first lens faceand the second concave face, wherein a first portion of the plurality ofsteering portions are configured to steer an incident electromagnetic(EM) beam in a first axis, and a second portion of the plurality ofsteering portions are configured to steer the incident EM beam in asecond axis, wherein each of the plurality of steering portionscomprises: a bulk substrate portion comprising an electro-opticalmaterial, wherein the bulk substrate portions corresponding to the firstportion of the plurality of steering portions are traversed by theincident EM beam before the second portion of the plurality of steeringportions; and a corresponding high-side electrode electrically coupledto the corresponding one of the plurality of steering portions; and atleast one of an anti-reflective coating or a half-wave plate opticallyinterposed between an interface of at least one of the bulk substrateportions corresponding to the first portion of the plurality of steeringportions and at least one of the bulk substrate portions correspondingto the second portion of the plurality of steering portions.